So far I've seen several meanings of "weird/original". Just recapitulating a few in an attempt to get to a categorisation of some sort (my take on it, at least) :
Weird as in 'what were they smoking when they wrote this?' - Threshold, and some scenes of 'is there in truth no beauty' that almost seem psychedelic
Original concept: Darmok
Original as in breaking the fourth wall: Far Beyond the Stars
Taking Star trek in an unprecedented direction, reversing several 'standards' : Dancing in the pale Moonlight, and perhaps Star Trek III
Episodes with just a bizarre feel to them: Schisms, Masks, Emergence, Phantasms and several others. I would like to add voyagers The Fight to this one.
Original format: Kor mentioned there was no musical episode. That's true, but I always liked Voyager's Muse , where in a sense the episode attempts to retell part of itself in ancient Greek theatre format. EDIT: I now see it was mentioned already.
As for the claim that Star Trek hasn't been original since the 60's: was it original back even then? I can't answer that question since I'm not really grounded in science fiction from that era and before….