You'll be able to do drama wherever you go as there is a university-wide drama society (OUDS) and the majority of productions will be open to anyone from any college. Some colleges do have more facility to put on plays within college grounds than others but again it is likely that a lot of those productions will be open to anyone anyway. Many college drama societies exist more as funding bodies for student drama than as drama societies in the usual sense.
OUDS run as a funding body/centralised hub for drama but actual productions are put on by student production companies or college drama societies (usually still open to all though some may prioritise college members). Funding for student production companies comes from OUDS, college societies (which generally fund anything though may provide more for shows with college members on cast/crew), the Cameron Mackintosh Drama fund etc. and the tech society (OUTTS) have a very large array of set, props, lights and sound equipment to hire for very cheap so lots of theatre gets put on because there is a lot of money and resources to do it. There are venues around Oxford open to student productions, from the tiny Burton-Taylor Studio all the way to the Oxford Playhouse which is a large professional venue. Student productions bid for slots at these venues to put on shows. Some shows are also put on in college auditoriums where there may be less competition for performance slots.
Some college specific things I can remember include (this is from a couple of years ago though, and not exhaustive):
Queen's do a garden musical every year, though anyone can audition for this. I think it may be organised by Queen's students primarily though production teams for this generally include students from any college too. The drama society there is called the Egelsfield Players.
St John's College has a very nice auditorium which I believe students at the college can use for productions, though I don't think this is used widely by OUDS.
Corpus Christi where I studied has a drama society called Owlets which used to be very active before COVID. Quite a few of us have been working on bringing it back to life though so it may be thriving again in the future. Corpus also has an auditorium which is quite good for rehearsals and simpler performances.
LMH has the Simpkins Lee auditorium which is another nice college drama venue.
New has a drama society and a classical drama society which puts on a Greek play every year.
Pembroke does an annual musical in its Pichette Auditorium, I believe this is open for anyone to audition.
St Catherine's College appoints a Cameron Mackintosh Visiting Professor of Contemporary Theatre every year (past appointees have included the actor Adjoa Andoh and the director Sir Gregory Doran). They usually run lectures and workshops though these again tend to be open to anyone. Catz also has a music house and auditorium that students there can use and the drama society there has put on musicals in the past.
Worcester College has a drama society called the Buskins, which tends to do garden plays and act as a funding body.
Wadham has a drama society that is very active including pantomimes, garden plays, new writing and Shakespeare. You may be sensing a theme here but generally anyone from any college can audition for these too.
Many colleges will do a garden play every summer, searching the college name + garden play might help you find out about this.
The VAST majority of drama opportunities at Oxford, even those run by college drama societies, are open to all. It can help to be at a college with good drama facilities as it is much easier to book a theatre space if you are a member of the college where it is (though Keble and Balliol have theatre spaces that are bookable by anyone via OUDS). It can also be easier to get funding for OUDS productions from the drama society you are affiliated with e.g. Owlets gave £50 grants only to productions with Corpus involvement, everyone else could only get loans.
Sorry if that was WAYY too much information but I hope this helps!