"What do I expect to hear in a folk club...?"

To be honest, I'm happy to hear pretty much anything and everything that entertains me.

What did I actually hear in the late 60s and 70s, around Sheffield?

Child's and other collector's, traditional ballads in what appeared to be
Re-worked versions of these based largely, but not completely, on what Ashley Hutchings was doing.
Music Hall songs.
Stuff written by contemporary folk artists, including (as examples), Dylan, Lightfoot etc.
Tom Lehrer stuff
Acoustic blues.
Acoustic versions of pop songs.
Folk rock (rare though it was).
British dance music.
Skiffle.
Irish, Scottish, English, Welsh and Manx songs, so obscure that people couldn't remember who wrote them (i.e., proper folk music).
People performing unaccompanied songs (often using crib sheets.
Recitations, often using crib sheets). Note cribbing was always better than continually forgetting the words.
Songs made up by the people wot sung 'em.
Professional performances by folk stars, such as Martin Carthy, Mike Harding and that Jones chap (who was always amiable).
By 'eck, them wer't days

It would be easier to define what wasn't acceptable, rather than what was and that varied from club to club. One of the joys was that anything went. Another feature as that it didn't have to be perfect.
generally, it was us (we, the folk implied in the phrase "folk music") entertaining ourselves in our own ways.