One of the strangest games I've played must be Aaargh! An extraordinary title, this game is about a dragon and an ogre competing about eggs. You play as either the dragon or the ogre, both having different advantages.
As a dragon, you run around the village destroying houses while the villages are trying to defend themselves. If I recall correctly you can eat the villages to gain some momentum.
In one of the houses there is a giant egg. Once you find the egg you need to fight the Ogre for it.
There are 6 different levels to explore in order to collect all the eggs. What happens then, I do not know, because I never got that far.
Oldie but goldie. This game makes Suda 51 games' seem sane.