Are you university based or not? You could consider a College chapel choir (which may be happy to have you even if you're not a student) and they cover most possible standards! If you're good, you could see if there are any vacancies at University Church SMV (on the High St).

There are university chamber choirs, and again they sometimes allow non-students and if you're good enough that the thought of an audition doesn't terrify you they can be a very good option.

Town-wise there's the Oxford Bach Choir (huge but good reputation), Commotio, Jubilate! (both chamber choirs), The Oxford Gospel Choir, Pro Musica (hot on sight-singing), tons of Come-And-Sing ad hoc things, The Oxford City Singers (non-auditioning) and I'm sure lots more.

For links/contact details see the bottom of the Daily Info concert guide:
http://www.dailyinfo.co.uk/events.php?colname=Concert#links
I would strongly recommend going to some concerts and seeing for yourself what you like the look (sound!) of. Oxford is much more open than Cambridge in terms of joining in with things, even university-based. It does also mean the quality is a little wider in range, but as soon as you've got a foot in the singing world you'll get a sense of what's what and who's who, and probably be inundated with requests to sing, usually at short notice!

I think the Bach Choir is very demanding. A friend, a good singer, was chucked out because her sight-reading was not good enough.

"A friend, a good singer, was chucked out because her sight-reading was not good enough."

That's disgraceful!!!!! And exactly the reason that choirs like The Oxford City Singers exist!

If you mean classical choirs, sight-reading, formal concerts you've had some great answers. East Oxford Community Choir, meets St Albans, Charles St off the Iffley Rd Sunday lunchtimes, is an informal version of that style. If you mean world music, learning by ear, check out http://www.naturalvoice.net, look for Oxfordshire and you'll find Joined-up Singing, ( Mondays by the J.R. ) Sounds Fun, ( Tuesdays off the High St ) and various others. Useful for one-off events too.

What about any opera groups?