Did the Pandavas eventually take rebirth? If they did, who were they and what happened to them?
Arjuna was reborn as Kannappa Nayanar, one of the 63 great Shiva-bhaktas in South India. When Arjuna fought with Lord Shiva as a Kirata to obtain the Pasupatastra, he had at first insulted him based on his caste (although later he admired the hunter). And after realising who He really was, Arjuna fell at Mahadeva's feet and repeatedly asked for his grace. Therefore, as a combined result of this, Mahadeva told Arjuna that he will have to take another birth, but will live only for sixteen years. He would perform Shiva-bhakti for six days, and return back to His abode. Thus, Arjuna was born as Kannappa Nayanar.
No Arjun didn't take rebirth. In fact he attained Vaikunta , the highest of all positions . The Mahabharata itself clearly mentions it. In Gita Krishna himself describes that no one is dearer to him as Arjuna. In fact Krishna-Arjun were Nara-Narayana. There is no question of rebirth for Arjuna. The story of Kannappa is different . As per original Mahabharata, Arjuna attained Vishnu Loka
He beheld Govinda endued with his Brahma-form. It resembled that form of his which had been seen before and which, therefore, helped the recognition. Blazing forth in that form of his, he was adorned with celestial weapons, such as the terrible discus and others in their respective embodied forms. He was being adored by the heroic Phalguna, who also was endued with a blazing effulgence. The son of Kunti beheld the slayer of Madhu also in his own form. Those two foremost of Beings, adored by all the gods, beholding Yudhishthira, received him with proper honours.
It is detailed in the Bhaviṣya Purāṇa in this section:
....At this Shiv said - "Because you are all the devotee of Shree Krishna that is why I am protecting you otherwise you were all worth of being killed. You all will have to suffer for this by taking birth in Kali Yug." and he got disappeared....
... Although my words will not be a lie, still Pandavas and Kauravas will be born on Prithvi (earth) from their part and will be free soon. Yudhisthira will be the son of Vats Raaj (Bacchraj), his name will be Baalakhaani (Maalkhan) and he will the king of Shireesh (Sirsa) city. Although, he spoke bad languages, Bheem's name will be Veran and he will be the king of Vanaras. Whoever will take birth from Arjun's part, he will be my Bhakt and great intelligent. He will be born in Parimala’s house and his name will be Brahmaananda. Nakula will be born as Ratnabhaanu (Raatibhaan)’s son in Kanyakubja and his name will be Lakshmana. Sahadev will be the son of Bheem Sinh and his name will be Dev Sinh. Dhritraashtra's part will be born as Prithviraaj in Ajmer and Draupadi will be born as Velaa, the daughter of Prithviraaj. The great donor Karna will be born as Taaraka (Saadar/Tahaar). At that time I will also take Avatar in the form of Raktabeeja. Kauravas will be skilled in Maya war and Pandavas will fight according to Dharma."
It feels weird having to defend a text from the main canon, but the Bhaviṣya Purāṇa is affirmed in the Padma Purāṇa to be a Mahāpurāṇa, putting above even celebrated texts like the Devī Bhāgavata. Also, the people who refute it couldn't even figure out Gabriel's very obvious appearance and central importance to the plot, so they don't understand the story well enough to be an authority to refute it. They also always ignore that there are two very obvious references to Christianity and Islam at different points in the story, not one for each, so I really doubt they even read the thing.
P.S. Having read most of this section it seems like Harinagara is the avatar of Viṣṇu that was promised much earlier to Kali to protect the wicked Gabriel, after his ardent prayers (I am going to assume they are one and the same due to their extremely similar qualities and stories focusing on them neighboring each other). That seems like a fun pseudo-horror story to tell round a campfire.
Both Kshattri and king Yudhishthira entered into the god of Righteousness.
Yudhisthira, in the end, merged in to Yama.
"He also beheld the princess of Pancala, decked in garlands of lotuses. Having attained to Heaven, she was sitting there, endued with a form possessed of solar splendour. King Yudhishthira suddenly wished to question her. Then the illustrious Indra, the chief of the gods, spoke to him, ‘This one is Sree herself. It was for your sake that she took birth, as the daughter of Drupada, among human beings, issuing not from any mother’s womb, O Yudhishthira, endued with agreeable perfume and capable of delighting the whole world.
Drauapdi was in heaven and became Sri.
In another part he beheld Bhimasena of great puissance, sitting in the midst of the Maruts, and endued with a blazing form. He was sitting by the side of the God of Wind in his embodied form.
Yudhisthira sees Bhima with Vayu, meaning, he is in Vayu Loka.
Vaishampayana said, "King Yudhishthira, thus praised by the gods, the Maruts and the Rishis, proceeded to that place where those foremost ones of Kuru’s race were. He beheld Govinda endued with his Brahma-form. It resembled that form of his which had been seen before and which, therefore, helped the recognition. Blazing forth in that form of his, he was adorned with celestial weapons, such as the terrible discus and others in their respective embodied forms. He was being adored by the heroic Phalguna, who also was endued with a blazing effulgence. The son of Kunti beheld the slayer of Madhu also in his own form. Those two foremost of Beings, adored by all the gods, beholding Yudhishthira, received him with proper honours.
Yudhisthira sees Arjuna and Krishna together in heaven.
In place belonging to the Ashvinis, the delighter of the Kurus beheld Nakula and Sahadeva, each blazing with his own effulgence.
Yudhisthira sees Nakula and Sahadeva with Ashvins
In the end, the Pandavas have attained to their highest end and there is no mention of their rebirth.