Correct version of sharabh story is found in padma purAna, uttar khanD chapter 18:
Then the demon (jalandhar) was struck on his chest with a spear by shiv. From his mouth fearful and yawning jvar emerged. He having the face of a lion and a human figure was (called) vIrjvar.
Seeing jvar having a lion’s face, moving out of the demon’s body, (shiv) made a ‘hum’...
DashAvtAr is an interpolation in later puraNas (i.e. these puraNas limit avtArs of vishNu).
In rAmAyan and mahAbhArat, 20+ avtArs of vishNu are mentioned like kapil, hayagrIv, prithu, hamsa, nar-nArAyaN-hari-krushNa, dattAtreya, dhanvantri, etc.
Even shesha is cosidered an incarnation of vishNu (and not attendant of vishNu as people believe) in itihAs and ...
The original and detailed version of hamsa (swan) avtAr is found in mahAbhArat shAnti parva (book 12), chapter CCC . It is a discourse between sadhyas and swan :
bhIshma said, 'In this connection I shall recite to thee an old narrative, O yudhishthir, of the discourse between the Sadhyas and a Swan. Once on a time the Unborn and eternal Lord of all creatures ...
Garuda Purana Skanda 1, Chapter 1, sloka 29 states:
ततः सप्तदशे जातः सत्यवत्यां पराशरात् । चक्रे वेदतरोः शाखां
In the 17Th incarnation god came as the son of Sathyavati and Prashara
seeing men defecient in knowledge he branched the tree of veda.
And, Srimad Bhagavatam Skanda 1, Chapter 3, Sloka 21 states:
ततः सप्तदशे जातः ...