Possibly The Demu Trilogy by F.M. Busby?
Some points that match:
1980's sci-fi novel
Partial check. The first and second novels in the series were published in the 1970s. But the Trilogy omnibus (including the last novel) was published in the 1980s and may the version you first encountered.
with multiple races
Check. Starts with Barton (MC) in the hold of a strange space craft with about 50 other people; some of them humans, the rest hominoids of various stripes.
involved in an Interstellar war
Check. It is an ideological conflict. The alien Demu consider themselves the only real people in the universe. They capture members of other races and operate on them extensively to make them look as Demu as possible.
A man on one of the space ships gets caught along with his crew and placed in a prison.
Partial check. Starts with Barton (MC) in the hold of a strange space craft with about 50 other people; Not his crew but more than himself. He is then put in a prison by the Demu.
He eventually manages to escape along with a female from another race by stealing a craft.
Check. He escapes with an alien female Tilari named Limila and steals a spacecraft to return to human space.