For girls at Clare, the dress code was a black skirt/trousers and a shirt (most people wore white, but some wore coloured shirts or a white top) for matriculation.
Ok...formal hall and "formal dinners..."
Formal hall happens most nights of the week in most colleges (the exact number varies; some places have it every night, some only once/twice a week). You go there instead of normal dinner, if you want to, normally for special occasions or formal swaps with other colleges but you have to book a ticket in advance. You have to be smartly dressed, but not OTT. At Clare, men need to either wear a suit, or a gown over normal smartish clothes. Girls can get away with more, just as long as you look smart. Gowns are compulsory at some colleges, not at others.
Formal dinners is not really a specific term. Various societies and subject groups will have an annual dinner (or in the case of college boatclubs, a termly carnage fest disguised as a dinner). For these you will need black tie (DJ and bow tie), and girls will need either a nice evening dress (but not a ballgown) or a pretty skirt and top. For the May Ball, black tie (or white for certain colleges) is essential, and ball dresses/evening dresses for the girls, I'm a little hazy on the exact definition.
Girls spend more than boys on these things because you can't
wear the same dress in the same company twice!
Fortunately I have a few left over from U6th when everyone was having posh 18th birthdays, so have only bought one new dress this year (only £15!
) plus a skirt and various tops.