Ok, well after having this problem several times, I found somthing that works.

All you need is a soldering iron.

Take out all the screws you can, and on the stripped or stubborn ones, stick the tip onto the screw head. Count to 5 and pull up on the pickguard, and the screw should go through the pickguard. I havent hurt any of my pickguards yet, so you shouldnt either. One The pickguards off, then grip the screw with some vice-grips or the like, and back it out.

Hope this helps someone.
i know this is an old thread but anyone have any experience doing this? does it actually work?
I want to clean the pots on my sg but one of the screws on the back plate is completely stripped on the head, and a bit rusted. I've tried so many things, including an electric drill/screwdriver, nothing works. I am considering trying this.
what he did was heat up the screw enough to melt the pickguard when he pulls up on it. I would use needle-nose pliars and try to grip the screws that way first before putting a bigger hole in your pickguard
yep I just did it, and it worked. Been trying to get this screw out for weeks. It took a little longer than I thought to solder through but it worked eventually, and I used pliers to twist the screw out.
ok, so i've never had to get the screw out of a guitar, but in other situations, I've used a small chisel and a ball peen hammer, basically, you just get the chisel and put a small indent in the edge of the screw and tap the screw around softly with the hammer.
I assume this would work perfectly, as it works in mechanics with corroded steel.