I've played lots of odd games but the one that stands out is Freak Out, you play as a little girl with a posessed scarf that that you can use as a weapon and pick stuff up with it, I remember in particular a level where there were lots of women walking around with hugely oversized boobs and you had to use the scarf to pop them, or something like that.
For me it was this obscure Japanese Hentai game a friend had downloaded illegally on to his computer. It was called Battle Raper II. I kid you not, that is the actual title. And it is pretty much exactly what you're probobly now imagining it to be.