Though there are Avatars of God in Hinduism, none of them are immortal, except Parashurama.
Immortals of Hinduism are very interesting.
They Seven are,
“Ashwathaama Balir Vyasaha Hanumantha VibeeshanahaKripa ParashuramaschaSaptaitey Chiranjivinaha”
1.Aswathama-Son of Dronacharya.
2.Mahabali who was slain by Lord Vishnu in the Avatar of Vamana/Trivikrama.
3.Vyasa-who compiled the Vedas and wrote the Mahabharata,some consider him as an avatar of Vishnu, though his name does appear in the ten Avatars of Vishnu.
4.Hanuman-Disciple and devotee of Rama .
5.Vibheeshana-Brother of Ravana, who defected to Lord Rama.
6.Kripa-military guru of the princes in the Mahabharata.
7.Parashurama-Avatar of Vishnu.
The common criteria for all the immortals is Bhakthi, surrender to God.
All of them are the devotees of Lord Vishnu, except Parashurama, who was a devotee of Lord Shiva.
For Aswathama, Immortality has been granted as a Curse.
Post follows on this.
In addition to this there are eight more Immortals.
Jambavan, Markandeya, Devapi, Maru, Saptarishis, Bhusunda (Crow),Banasur(son of King Bali) by Boon of Shiva, and Udal.
Of these eight Chiranjeevis, Udal seems to be an interpolation after 13th Century.
“Udal (full name Udai Singh) was a Rajput general in the army of Chandel King Maharaj Parimard Dev Burman (also known as Parmal or Parimal) of Mahoba in 12th-13th century AD. He was younger brother of Alha. Parmal raised Udal as his own son, since he was born after the death of his father Dassraj, who – a general himself – was killed in the service of Parmal(wiki)