Weirdest job interview I ever had was years ago for an internship with the Army Corps of Engineers. 250 of us had applied, 70 got through an initial screening process, one of them being me even though I'd never taken an engineering class. First off, they interviewed two of us the same time, for the one position. And the interview was done by four men with crew cuts and white shirts. And I was at the time a faux hippy dude with hair down to the middle of my back. Immediately knew that the interview was a waste of time. Which releived all stress and put me entirely at ease. The other guy really, really wanted the job and could hardly stop talking. I couldn't care less so gave calm and cogent responses, just killing time.

And of course they hired me.