I do know that area a bit but not sessiuns...there are at least a couple of pubs in Oxford that have live music though and at least one of them has folkier stuff...I will try to remember the name of it. I think it is in the area of the Magdalene bookshop...Banbury's pubs seem mostly for footballers sadly, or play disco music. Does that place with the Cromwell room have live music?
There's a nice traditional pub nearby in Deddington; try that?

good luck! I love that area. There must be a sessiun happening somewhere...