I've heard that interviewers ask strange, out-of-the-blue questions to catch students off-guard. How do I circumvent this?

Ultimately, all tutors are trying to do in interviews is determine how well you would fit in in the Oxbridge teaching environment - an environment that is designed to challenge you and push you to the limits of your knowledge. So it would make sense for interviewers to try to emulate this in interviews. Having said that, the idea that that interviewers ask strange questions to try to catch you off-guard is a misconception - sometimes strange questions are asked, but these are actually a part of a wider discussionIn my second interview, I was asked 'Should the government have the legal right to seize one of your kidneys to sell off if you go bankrupt?'. Out of context, that question seems absurd. However, it came as the conclusion to a long discussion about what counts as a possession and what one can and cannot legally give away. Thus the best way to avoid being caught off-guard is to think proactively in your interviews; don't be afraid to defend your opinions, but also don't hold onto them in the presence of overwhelming contrary evidence. If you talk your interviewers through your thought process and give them a good insight into how you think, you maximise your odds of getting an offer.