Hello Deneb,

Yes, there's lots and lots!

The Half Moon session is still going on Sunday nights.
http://halfmoonoxford.com/

Other sessions at The Isis (2nd Friday of the month for "The Bastard English Session" (ie fairly broad range of interpretative styles) and a Sunday afternoon session, too (although I can't remember which Sunday of the month).

Oxford Folk Festival, The Folk Club and Oxfolk have already been mentioned (www.oxfolk.org.uk, btw :-)

Oxfordshire Folk Association
www.oxonfolk.co.uk
is comprehensive, especially for dance clubs, but not completely up to date. Daily Info - www.dailyinfo.co.uk - is really good for events in general.

Hope you find something you enjoy.