Vishnu’s fifteenth avatar is Vamana. Vamana means dwarf. Bali was an emperor, son of Virochana and grandson of Prahaladha (refer Narasimha avatar) He was killed in a battle with Indra, but resurrected by Sukra, the guru for demons. Bali performed various yajnas and attained superior prowess. Bali started a huge fire ritual. If he attains more prowesses through this yajna, gods have no option except to flee. Agni, the god of fire (God of fire, Agni is invoked in all fire rituals like yajna. Agni is the carrier of oblations offered in the yajna to Gods and Goddesses) and other gods met Vishnu and sought His protection. Bali used to give whatever is asked for from him. Vishnu was born as a dwarf to sage Kashyap and his wife Aditi. When the divine dwarf grew up, He reached the sacrificial place where Bali was performing Ashvamedha yajna. Bali on seeing the shine of divinity around Vamana, welcomed Him. Bali offered to give Vamana whatever is asked for. Vamana asked for earth measureable by three steps of His feet. Sukra, the guru for asuras (demons) warned Bali that the dwarf is Vishnu only. Bali said out of arrogance and ego “It is the Lord that begs from me”. Lord Vamana grew in size and won over all the three worlds ruled by Bali. Finally, Vishnu blessed Bali because of his various auspicious deeds. There is an Upanishad by name Varaha Upanishad that contains teaching of Lord Varaha, mostly on realizing the Brahman (Valmiki Ramayana – Bala Kanda - Canto 29 and Narayaneeyam cantos 30 and 31). Vishnu’s famous three steps are cited in Vedas too. (The first stride is the Earth. The second stride is the visible sky. The third stride cannot be seen by men and is the heaven where the gods and the righteous dead live.)
Sixteenth incarnation of Vishnu is Parasurama, a brahmin sage. He was born to Jamadagni and Renuka in the linage of sage Brighu. Parasu means axe. He did penance to please Shiva who gave Him the famous axe. In this avatar, Vishnu incarnates himself as a brahman Shiva. He incarnated to avenge all kshatriyas (class of warriors) who were suppressing the Brahmins (knower of Vedas). He was born with strange physical power, and became a great fighter. Kartavirya a powerful king, once went to Jamadagni's home and stole the Kamadhenu cow, which was giving infinite quantity of milk. Jamadgni was enraged and he went and killed the king and brought Kamadhenu back. On hearing this, son of the king came back and killed Jamdagni. Parasurama was enraged at this and avenged the death of his father by killing kshatriyas in 21 battles. Lord Rama and Parasurama (both are incarnations of Lord Vishnu) meet each other face to face in Valmiki Ramayana. Parasurama is a short-tempered sage. He chopped off His mother’s head, who was however resurrected immediately. (Valkimi Ramayana – Bala Kanda 74 and 75, Bhagavata IX.15, 16 and Narayaneeyam canto 36)
Seventeenth incarnation of Vishnu is sage Vyasa. He was born to sage Parashara and Satyavati. He was responsible in dividing The Vedas into three branches Rik Veda, Yajur Veda and Sama Veda (Some citations also include Atharva Veda). Atharva Veda is considered as subsequent origin. He has also authored 18 great puranas (epics), Brahma Sutra, Srimad Bhagavata (which includes Bhagavad Gita) and Mahabharata. Vyasa is one among the eight ‘siranjeevis’ (immortals). The other seven are Aswathtama, Hanuman, Kripachairar, Maha Bali (discussed under 15th incarnation Vamana), Vibishana (brother of Ravanaa), Markendeya, Sage Vyasa and Parasurama (the last two being incarnations of Lord Vishnu). The main purpose of this incarnation is to improve the quality of humanity making them to do more and more virtuous acts. This incarnation was mainly spent on writing highly valuable reading materials.