What can I do about nasty comments in student evaluations that could cause me to get fired?
To answer this question: "Can the students be held responsible for their lies? The questonnaires are anonymous but they were done online so it would be possible for the institution to find out the identities of the students."

Probably not.  If the university promised the students their comments were anonymous, then it probably cannot reveal their identities, which would rule out holding them responsible.  Most likely the university did not retain records of who wrote which comments, so as to protect itself against accidental disclosure or subpoenas seeking to deanonymize the comments.