Student representation is important and to that end the Mathematics Undergraduate Representation Committee (affectionately known as MURC) forwards your views and suggestions to departmental committees. They have produced a Freshers' Guide (Fresher is the name for a first year student) and run an annual bookstall.
Your college is a great place to socialise, but you might also want to socialise with mathematicians from other colleges. There are two societies for mathematicians at Oxford:
The Oxford Invariants
The Invariants are the Oxford University student society for Mathematics. They host informal lectures, often given by leading mathematicians, as well as socials and puzzle competitions. They also produce a termly magazine and you can find out more about them on their website.
The Mirzakhani Society
The Mirzakhani Society is a society for women studying maths at Oxford - its aim is to support students through providing a space to discuss issues that women may encounter during their degrees. It holds weekly ‘Sip and Solve’ meetings with tea and cake, and other events such as socials and talks. You can find out more about the society on their Facebook page.