The weirdest question that I had was "What one word makes you stop and think?". Since there was Trekkie stuff in the office, I said "Spock!". I was hired. Months later, I asked him why he asked that question. He said that he wanted to have a word for each person that would grab our attention.
I also have been part of interviews where a totally unrelated type of questioing goes on. Questions like "What is your favorite cartoon character?" or "Have you ever gone to a restaurant for the eralybird special?" plus many more are often asked until the interviewee finally stops and says "What does this have to do with the job?". This is to find out how far a person may tolerate pursuing a ridiculous course of action.
When I interview someone for a tech position, I always ask them "If computers had not yet been invented, what line of work would you be in?". I refer to this question as my "Pirate Looks at 40 Question (Jimmy Buffett)". I have received responses such as used car salesman, florist, concert pianist and paramedic. This JB reference is because in that song, JB says that he is a Pirate, but the position is not available anywhere. So, I wonder what the person is interested in besides computers. BTW, my response is Financial Analyst.