It's not currently a massively active society (though maybe your year will make it one), but we have a BUMS dinner every year, which tutors and undergraduates go to. However, there are other social events - in first year you get (free) drinks with your tutors after tutorials once or twice a week. Plus a subject formal dinner at the end of each year. You should also be given a college parent or two, from amongst the second years, who are supposed to mentor you when you first get here.
Because there are only eight or so students per year, you will get to know your tutors and course-mates very well.
If you want a more involved maths society, the Invariants (Oxford undergraduate maths society) meet every Tuesday, and have weekly competitions and talks.