First of all there is not anything like 44 Avatars of Shiva. There are many (actually infinite) Avatars of Lord Shiva. Also as you have asked "What is the need of his avatar if his function is to just destroy the Universe?" So, I'm here describing Avatars along with significance of them:
Incarnations from Vedas:
Vedas talk of many incarnations of Lord Shiva. Within the avaliable Shakhas of Vedas today we can get more than 25 incarnations of Lord Shiva itself in the Vedas:
i) AshtaMurti Incarnations:
Eightfold manifestation of Lord Shiva through Brahma (Prajapati) are known as AshtaMurti avatar. It is described in this chapter of YajurVeda Shatapatha Brahmana. As we see in that chapter Brahma calls the incarnations as:
You are Rudra. You are Sarva. You are Pasupati. You are Ugra. You are Asani. You are Bhava. You are Mahadeva. You are Ishana.
He entered the Eight things and Brahma calls it as;
Rudra is fire. Sarva is water. Pasupati is plants. Ugra is air. Asani is Vajra. Bhava is Indra. Mahadeva is moon. Ishana is sun.
Thus these all things are just forms of Lord Shiva/ (AshtaMurti incarnation of Shiva).
Significance of AshtaMurti Avatar:
There is great significance of AshtaMurti Avatar and it is described by Brahma himself in the same chapter of YajurVeda. Those 8 incarnations made the whole world function as we see it today. As stated there Prajapati there states:
Fire became suchlike. Water became suchlike. Plants became suchlike. Air became suchlike. Vajra became suchlike. Indra became suchlike. Moon became suchlike. Sun became suchlike.
So, the significance is these Avatars made all these things such like. ie. AshtaMurti are the innate power of all these.
ii) Ekadash Rudra incarnations:
Vedas also define the 11 Rudras which are known as Ekadash Rudras. BrihadAranyaka Upanishad which is itself a part of Shatapatha Brahmana of YajurVeda. It's defined in the Brihadaranyaka Upanishad 9.4. The names aren't given there, but from Mahabharata we know their names as:
They were Mrigavayadha, Sarpa, Niriti of great fame: Ajaikapat, Ahivradhna, and Pinaki, the oppressor of foes; Dahana and Iswara, and Kapali of great splendour; and Sthanu, and the illustrious Bharga. These are called the eleven Rudras. [Sambhava Parva chapter 66]
Significance of Ekadash Rudra Avatar:
Just as AshtaMurti avatar has their form as Agni, Vayu, Surya, Chandra etc.. similarly Ekadash Rudra also have great significance and they rule over Pranas and Atman. BrihadAranyaka Upanishad 9.4 explains it as:
"Which are the Rudras?" asked Sakalya.
" The ten Pranas in the body, with the Atman as the eleventh. When they depart from this mortal body, they make one's relatives weep. Because they make them weep (rud), therefore they are called Rudras.
Thus as clear from above Ekadash Rudras rule over Pranas and Atman in the body.
iii) PanchaBrahman incarnations:
As I discuss in my answer here Vedas also talk of 5 fold manifestation of Lord Shiva which are called PanchaBrahmans. It is in Yajurveda Taittariya Aranyaka 10.17.1 to 10.21.1. Names of PanchaBrahmans are:
Sadyojata, Vamadeva, Aghora, Tatpurusha, Ishana.
Significance of PanchaBrahman avatar:
As I discuss in the same answer
Significance in Cosmic level:
Ishana➡ Kshetrajna and enjoyer of Prakirti
Tatpurusha➡Gunas of Prakirti
Aghora➡ Cosmic Intellect (Buddhi)
Vamadeva➡Ego (Ahamkara)
Sadyojata ➡ Mind (Mana)
Significance in bodily and elementary level:
Ishana➡ Ether, Sound, Ear, Mouth
Tatpurusha➡ Air, Touch, Skin, Hands
Aghora➡ Fire, Colour, Eyes, Legs
Vamadeva➡ Water, Taste, Tongue, Anus
Sadyojata➡ Earth, Smell, Nose, Sex Organs.
iv) Rudra Avatar:
Incarnation of Rudra/Mahadeva is one of the most famous incarnation of Lord Shiva. His primary function is to be the destroyer and to destroy arrogance of Devatas. This incarnation also takes place through Brahma and is described in this chapter of Atharvaveda:
व्रात्य आसीदीयमान एव स प्रजापतिं समैरयत् ।।
स प्रजापति: सुवर्णमात्मन्नपश्यत्तत्प्राजनयत् ।।
तदेकमभवत्तल्ललाममभवत्तन्महदभवत्तज्जेष्ठमभवत्तद्ब्रह्माभवत्तत्तपोऽभवत्तत्सत्यमभवत्तेन प्राजायत ।।
सोऽवर्धत स महानभवत्स महादेवोऽभवत् ।।
स देवानामीशां पर्यैत्स ईशानोऽभवत् ।।
स एकव्रात्योऽभवत्स धनुरादत्त तदेवेन्द्रधनुः ।।
नीलमस्योदरं लोहितं पृष्ठम् ।।
नीलेनैवाप्रियं भ्रातृव्यं प्रोर्णोति लोहितेन द्विषन्तं विध्यतीति ब्रह्मवादिनो वदन्ति ।। [Atharva Veda 15:1]
There was Vratya . He roused Prajapati to action. Prajapati beheld gold in himself and engendered it. That became unique, that became distinguished, that became great, that became excellent, that became Brahman, that became Tapas, that became Truth: through that he was born. He grew, he became great, he became Mahadeva. He gained the lordship of the Gods. He became Ishana. He became Eka Vratya. He held a bow, even that Bow of Indra. His belly is dark-blue, his back is red (Nila Lohita). With dark-blue he envelops a detested rival, with red he pierces the man who hates him: so the knowers of Brahman say.
His AshtaMurti are his Adhisthata in various direction as described in this chapter of Atharvaveda:
Bhava from eastern. Sarva from southern. Pasupati from western. Ugra from Northern. Rudra from Nadir. Mahadeva from zenith. Ishana from intermediate regions.
Significance of Rudra Avatar:
Rudra Avatar is also of great significance. Several deeds of Rudra Avatar are described in Vedas like:
➡ Punishing the arrogant Devas:
In this kanda of Taittariya Samhita of YajurVeda Devas are punished when they exclude Rudra from sacrifice;
The gods excluded Rudra from the sacrifice; he pierced the sacrifice, the gods gathered round it (saying), 'May it be right for us.' They said, 'Well offered will this be for us, if we propitiate him.' That is why Agni is called the 'well offerer' (svistakrt). When it was pierced (by him) 3 they cut off (a piece) of the size of a barleycorn; therefore one should cut off (a piece) the size of a barleycorn. If one were to cut off more, he would confuse that part of the sacrifice. If he were to make a layer and then to sprinkle, lie would make it swell on both sides. He cuts it off and sprinkles it; there are two operations; the sacrificer has two feet, for support. If he were to transfer it (to the Brahman) crosswise, he would pierce the unwounded part of the sacrifice; lie transfers it in front; verily he transfers it in the proper way. They transferred it for Pusan. Pusan having eaten it lost his teeth; therefore Pusan has pounded food for his share, for he has no teeth. The gods said of him, 'He has lost (his teeth), he is not fit for the offering.' They transferred it to Brhaspati. Brhaspati was afraid, 'Thus indeed will this one fall on misfortune.' He saw this Mantra; 'With the eye of the sun I gaze on thee', he said, for the eye of the sun harms no one. He was afraid, 'It will harm me as I take it.' 'On the impulse of the god Savitr, with the arms of the Açvins, with the hands of Pusan I take thee', he says; verily, impelled by Savitr, he took it with the holy power (Brahman) and with the gods. He was afraid, 'It will harm me as I eat.' 'Thee with the mouth of Agni I eat', he said, for nothing harms the mouth of Agni. He was afraid, 'It will harm me when I have eaten.' 'With the belly of the Brahman', he said, for nothing harms the belly of the Brahman. 'With the holy power (Brahman) of Brhaspati', (he said), for he is fullest of the holy power (Brahman).
➡ Punishing Brahma:
In this chapter pf Shatapatha Brahmana of YajurVeda Rudra punishes Brahma as:
Pragâpati (Brahma) conceived a passion for his own daughter... 'May I pair with her!' thus (thinking) he united with her. This, assuredly, was a sin in the eyes of the gods. 'He who acts thus towards his own daughter, our sister, [commits a sin],' they thought. The gods then said to this god who rules over the beasts (Rudra), 'This one, surely, commits a sin who acts thus towards his own daughter, our sister. Pierce him!' Rudra, taking aim, pierced him.
➡ Becoming Lord of Pashus:
As I discuss in my answer here YajurVeda describes how Rudra became PashuPati during Tripura Samhara;
They made ready an arrow, Agni as the point, Soma as the socket, Visnu as the shaft. They said, 'Who shall shoot it?' 'Rudra', they said, 'Rudra is fierce, let him shoot it.' He said, 'Let me choose a boon; let me be overlord of Pashus.' Therefore is Rudra overlord of Pashus. Rudra let it go; it cleft the Tripuras and drove the Asuras away from these worlds. [YajurVeda 6.2.3]
And there are other many significances of Rudra avatar besides these. Like destroying the Universe during Pralaya and so on as described in Smritis.
Thus 25 Avatars of Lord Shiva are described in Vedas and they are:
8 AshtaMurti Avatars + 11 Ekadash Rudra Avatars + 5 PanchaBrahman Avatars + 1 Rudra Avatar.
Actually there are other types of Rudras also described in SataRudriya section of YajurVeda, but trying to describe all of them will make answer extremely long.
Incarnations in Smriti:
Smritis (Puranas, Itihasas) also talk of many incarnations of Lord Shiva. Some, of them are:
i) 28 Yogesvara Avatar in this Manvantara:
As described in answer here there are 28 Yogesvara incarnation of Lord Shiva and they take place in every Dwapar and are:
Sveta muni, Sutaara, Damana, Suhotra,
Kanka, Lokaaksi, Jaigeesaavya
Dashivaahana, Rsabha, Brgu, Kaali, Puru,
Bali, Gautama, Vedavarsin, Gokarna Grhasvami, Sikhandi, Jaatimali, Attahas
Daaruka, LaanguliBheema, Sveta, Sooli,
Dandi, Sahinsu, Somasarma, Yogatma
Significance of Yogesvara Avatar:
These Avatars come with purpose that they teach Yoga to some rare souls and thus they can reach Rudra Loka from where there is no return. It is described in the same chapter of Shiva Purana.
ii) Other specific incarnations:
There are many other specific incarnation of Lord Shiva for specific purpose. They are described from chapter 6 to chapter 37 if SatRudraSamhita of Shiva Purana. They are:
1) Incarnation of Ardhanarishwara:
➡Described in SatRudra Samhita Chapter 3
➡Incarnation of Lord with half female.
➡For the starting of copulatory reproduction.
2) Incarnation of Nandi:
➡Described in SatRudra Samhita Chapter 6 and 7.
➡As boon to Silada, Lord Shiva borns as his son.
3) Incarnation of Bhairava:
➡Described in SatRudra Samhita Chapter 8 and 9
➡To detach 5th head of Brahma and latter to remain as protector in Kashi and to devour sins of those people who reach Kashi.
4) Incarnation of Sarabha:
➡Described in SatRudra Samhita Chapter 11 and 12.
➡ To control Ugra Narasimha from destroying the Universe.
5) Incarnation of Grihapati:
➡Described in SatRudra Samhita Chapter 13, 14 and 15.
➡Lord Shiva incarnates to become son of Visvãnara as Grihapati due to boon given to him.
6) Incarnation of Yaksheswara:
➡Described in SatRudra Samhita Chapter 16.
➡Gods become arrogant after getting Amrita in Samudra Manthan. Lord Shiva to subdue their arrogance assumes form pf Yaksha and gives a piece of straw to Gods. The fire God can't born it, wind God can't move it, Indra can't destroy it and so on. It is also described in Kena Upanishad.
7) Incarnation of Durvasa:
➡Described in SatRudra Samhita chapter 19.
➡ Various roles like Triggering of event of Samundra Mantha, separating Rama and Lakshmana, making Krishna invulnerable from Astras, giving boons to Kunti, cursing and blessing of many sages, Kings etc..
8) Incarnation of Hanuman:
➡Described in SatRudra Samhita Chapter 20.
➡To help Lord Rama in Ramayana.
9) Incarnation of Mahesha:
➡Described in SatRudra Samhita Chapter 21.
➡Urged by the friendship with Bhairava Lord Shiva incarnates as Mahesa to play with him.
10) Incarnation of Bull:
➡ Described in SatRudra Samhita Chapter 22 and chapter 23.
➡To bring back Lord Vishnu from Patala.
11) Incarnation of Pipplada:
➡Described in SatRudra Samhita Chapter 24 and 25.
➡To subdue the pride of Saturn and thus helping people to overcome affliction of Saturn.
12) Incarnation of Vaisyanatha:
➡Described in SatRudra Samhita Chapter 26
➡To redeem a prostitute named Mahananda who was devotee of Shiva, Lord Shiva goes to her house taking form of Vaishya and finally takes her to Shiva Loka.
13) Incarnation of Dvijaswara:
➡Described in SatRudra Samhita Chapter 27.
➡Test of king Bhãdryu by taking form of a Brahmin.
14) Incarnation of YatinathaHamsa:
➡ Described in SatRudra Samhita Chapter 28.
➡Test of a Bhilla (tribe race) by taking form of Yatinatha.
15) Incarnation of KrishnaDarshana:
➡Described in SatRudra Samhita Chapter 29.
➡Lord Shiva taking the form of Krishna Darshana shows that the part left after the Yajna also belongs to him, also Instructs Nabhaga.
16) Incarnation of Avadhutesvara:
➡Described in SatRudra Samhita Chapter 30.
➡Taking the form of Avadhuta Lord Shiva subdues arrogance of Indra and the birth of Jalandhara is triggered from this event.
17) Incarnation of Bhikshuvarya:
➡Described in SatRudra Samhita Chapter 31.
➡Dispells the suspicion of Brahmin women.
18) Incarnation of Sureshwara:
➡Described in SatRudra Samhita chapter 32 and also in Anushashana Parva of Mahabharata before Shiva Sahasranaama.
➡Taking the form of Indra Lord Shiva tested devotion of Upamanyu.
19) Incarnation of Jatila:
➡ Described in SatRudra Samhita Chapter 33.
➡Tests the Penance of Parvati by taking the form of Jatila.
20) Incarnation of Sunartakanata:
➡Described in SatRudra Samhita chapter 34.
➡Taking the form of Sunartakanata Lord Shiva goes to Himalayas house to ask hand of Parvati.
21) Incarnation of Sadhu Dvija:
➡Described in SatRudra Samhita chapter 35.
➡Gods being afraid that Himalaya will attain instant salvation due to giving of Parvati to Shiva request to Shiva to delay salvation of Himalaya. So, Lord Shiva taking the form of Sadhu Dvija goes in front of Himavat and start to insult Lord Shiva.
22) Incarnation of Ashwatthama:
➡Described in SatRudra Samhita chapter 36 and also in Mahabharata.
➡Destruction in the 18th night of Mahabharata war is carried out by Ashwatthama and so on.
23) Incarnation of Kirata:
➡Described in SatRudra Samhita chapter 37 and also in Vana Parva of Mahabharata.
➡Lord Shiva taking the form of Kirata tests the war skill and devotion of Arjuna.
iii) 12 Jyotirlinga Incarnations:
In the SatRudra Samgita chapter 42, 12 Jyotirlingas of Lord Shiva are spoken of. The incarnations in 12 Jyotirlinga are:
1) Somanath
2) Mallikarjuna
3) Omkareshwara
4) Mahakaleshwara
5) Rameshwara
6) Vishwanatha
7) Kedarnath
8) Trayambakeshwara
9) BheemaShankara
10) Ghusmeshwara
11) Nageshwara
12) Vaidyanath
The significance of the above Jyotirlingas are described in the links above.
Thus there are many incarnations of Lord Shiva. In this answer only I have named Eighty Eight Incarnations of Lord Shiva (25, 28, 23, 12). Coincidently it has become double of 44 incarnations which the question was asking. And there are many other incarnation of Lord too.
