A good tool for stubborn screws is an impact driver -- a steel cylinder with a holder in the front for various bits -- that you whack with a ball-peen. The impact drives the bit firmly into the screw, and also makes the tool turn very slightly. A couple of whacks is usually enough to break loose screws (or nuts -- it's 3/8 drive & will hold any socket). It sounds violent, but I was advised to buy mine to break loose screws in distributers holding points or condensors (remember those?), and it works very well for that, too.

Mine is a K-D, a popular maker of little specialty tools. Any decent parts store should have one, and they come with a selection of bits. They hold up pretty well -- I bought mine in 1973 ....