During homa we give food to Agni (pour oblations in fire) but how will that food reach those particular deva's?
Manusmriti 3.76 says:
- An oblation duly thrown into the fire, reaches the sun; from the sun comes rain, from rain food, therefrom the living creatures (derive their subsistence).
When it reaches the Sun, it means it has reached the abode of the Devas.
Your question is about how Agni delivers or transfers the food offered as oblations to the gods who are residing in Swarga loka or Dyu-Loka.
In Hinduism Agni is called as a messenger between earth and heaven. Agni receives the oblations offered on earth in Yajna , Homa etc. and transfers them to various gods residing in dyu loka or heaven.
मूर्धा दिवो नाभिरग्निः पर्थिव्या अथाभवदरती रोदस्योः |
तं तवा देवासो.अजनयन्त देवं वैश्वानर जयोतिरिदार्याय || RV 1.59.2 ||
mūrdhā divo nābhiraghniḥ pṛthivyā athābhavadaratī rodasyoḥ |
taṃ tvā devāso.ajanayanta devaṃ vaiśvānara jyotiridāryāya ||
2 The forehead of the sky, earth's centre, Agni became the messenger of earth and heaven. Vaiśvānara, the Deities produced thee, a God, to be a light unto the Ārya.
यो अग्निः करव्यवाहनः पितॄन यक्षद रताव्र्धः |
परेदुहव्यानि वोचति देवेभ्यश्च पित्र्भ्य आ || RV 10.16.11 ||
yo aghniḥ kravyavāhanaḥ pitṝn yakṣad ṛtāvṛdhaḥ |
preduhavyāni vocati devebhyaśca pitṛbhya ā ||
11 With offerings meet let Agni bring the Fathers who support the Law. Let him announce oblations paid to Fathers and to Deities.
In Shankhyayana Brahmana 3.6 Its said that Agni is mouth of gods. I.e. He is the mouth by which the Gods eat the sacrifice; and his flames are spoons with which he sprinkles the Gods, and he also consumes the offerings himself. oblations is poured in the mouth of agni who then becomes mouth of the gods
अग्निं प्रथमं देवतानां यजति | अग्निर्वै देवानां मुखम्।। ||
Agnirvai Devatanam Mukham
He is mouth of gods
Besides the another answer by which way agni transfers oblations offered here in homa to gods in Dyu loka is given by Adi-Shankaracharya in his commentary on The Brihadaranyaka Upanishad - Adhaya 6 - Brahmana 2 - Mantra 9 - "The Process of Rebirth" , where he is explaining the process of how food offered in Agnihotra Homa is transferred to Dyu loka.
These two oblations of the Agnihotra, after being offered, depart. They enter the sky, of which they make an Āhavanīya fire, with air as its fuel, and the sun's rays its white oblation. They offer libations to the sky and depart from there. They enter heaven, of which they make an Āhavanīya fire, with the sun as its fuel,’ and so on (Ś. XI. vi. ii. 6-7). Of course these oblations of the Agnihotra depart together with their accessories. Whatever accessories they are known to possess here, such as the Āhavanīya fire, fuel, smoke, cinder, sparks and the articles of oblation, they take along with them as they leave this world for heaven. There, although everything is in an undifferentiated state during the dissolution of the world, those ingredients retain their separate existence in an extremely subtle form—the fire remaining as fire, the fuel as fuel, the smoke as smoke, the cinder as cinder, the sparks as sparks and the articles of oblation as articles of oblation such as milk. That ceremony of the Agnihotra with its accessories, which never ceases to exist, but remains in a subtle form known as the Apūrva, reappears in its old form at the time of manifestation, by making use of the sky etc. as the Āhavanīya fire and so on as before. The ceremony of the Agnihotra is like that even to-day.
The process is in brief - When we offer oblations to gods in Yajna or Homa say like Agnihotra are consumed by Agni and then Agni himself acting as mouth of gods receives those on the behalf of gods.
The oblations offered are get converted and are carried out with the help of medium like smoke, cinder, sparks etc. leave the world for Dyu loka . But although they are converted they retain their sukshma rupa or extreme subtle form while. For them to reach to dyu loka there need some carrier , So they first enter into sky and they make the sky as fire with air as fuel and suns rays as oblations. From there they enter into heaven making heaven as fire and sun as fuel and so on..
Although the scope of the above citing of Brihadaranyaka Upanishad is different i.e. it is stating the process of rebirth , but from shankara's commentary we get a fair idea about how actually the food items are transferred to gods in heaven.