I would be looking at the wood you are screwing into. It sounds like you have a stud that is loose, and when you screw into it, it moves and is being pushed out of true by the screws.
I made a door jam to custom fit in an apt that's 100 years old. Door and jam is mortised properly, and was put together on saw horses, so there was no bind in hinges before I installed the door. The unit was together, just like I buy the complete units, and door works great, reveals even, but it pops when opening. Ive oiled hinges, and it fixes temporarily only. Ive taken screws out of the one that seemed to be popping, so if it was binded it would relax, then rescrewed hinge w/o goin into same holes, and it stopped, until I left like always! Ive built many door jambs, even a few doors, I build custom cabinets, furniture, etc... It's kinda embarrassing to have this problem that I usually fix in five minutes.
HELP!!