At interview they won't try and surprise you with something you can't reasonably have known. If they give you something new and outside of the curriculum, then they will explain it to you while you're there
You don't need to have participated in an Olympiad but it'd be a good thing to put on the personal statement. University admissions tutors look for engagement with your subject beyond the classroom so I'd definitely recommend, where possible, participating in an Olympiad, doing a maths based EPQ, reading a book about an area of maths that interests you and goes beyond the curriculum, to name just a couple of possibilities.
If you think you've got a reasonable shot at Oxbridge then you're likely to get into the rest of your choices as well, so I wouldn't be too worried about "wasting" a space.
You cannot apply to Oxford and Cambridge in the same application round, so you'll have to make a choice between them.