I had pretty severe strabismus at birth and also had muscle surgery shortly after. I was born in a developing country and the details of my condition at birth are nebulous, partly out of the ignorance of my guardians, understandably. Anyway, I'm pretty sure the surgery was done to ameliorate some amblyopia, because in North America, the ophthalmologist said wearing eyeglasses were useless that whole time (I'd been wearing them since an infant, basically). After that I had another surgery as a child and again as a teen.

Anyway, I also have what I like to describe as an underdeveloped stereoscopic vision. I can't see 3D movies either. Basically, my condition fits the OP's description.

When I tried out the Nintendo 3DS I also could not see it well, but I moved it at angles and kind of, barely could. However, I had to stop a few minutes later because it was giving me a massive headache (migraine-like).

I'm interested in Oculus Rift. I'll give it a whirl but I'm afraid it will induce that same head pain.

Has anyone with a similar condition experienced headaches in a similar situation?