Not sure how weird the concept is, but the parody/satire chat show was fairly popular in the UK. Dame Edna Everage was probably the best, as celebrities were disarmed by talking to an actor always in character (and in drag). But there were others where the character was more subtle, like Mrs Merton or Keith Barrett, and celebrities looked pretty uncomfortable at times.
Of course, Ali G (and Borat and Bruno) were probably the most extreme examples of parody interviews.
Not sure if interview segments (rather than shows) count. Dennis Pennis literally just went up and insulted celebrities, usually at red carpet premieres. And there were interviews conducted by puppets - such as Zig and Zag - that got celebrities confused and off guard. But I can't think of anything more recent that is like any of the above.