I have always enjoyed the hard, yet brittle alloy of an Exacto Blade.
These are small pointed 'razor blade' types available in most hardware and all hobby stores. For small screws, use the blade with about a 15 degree point (pointy) and work the tip into one of the obliterated slots of the former Phillips head screw with a small, firm, slicing motion. The harder alloy will cut the screw's alloy, then break off as you work ;-)
With patience, you'll have worked a slot into the screw head (similar to, yet finer than, the Dremel solution above) And the tip of the Exacto Blade will be just about the right size to use as a screw driver as in the Dremel solution; firm pressure to keep the tip in the slot, and back it out. If it snaps, get a new blade. Beware of loosing patience and making a mess of it(candid personal experience). The wider your new slot is, the better leverage you'll have in turning the screw (radius=lever in this case). If you can get some jewelers diagonal cutters to bite into the screw's periphery on each side, you'll have MAX leverage!
I haven't had to resort to messy oils, but a Liquid Wrench application may help. Also relieve any stresses on the screw (like re-tightening the ones around it) so you are only fighting one thing at a time. Bent sheetmetal parts are notorious for jamming screws; try to flatten them first. Or better yet, turn the sheetmetal to free the screw, if possible! The screw also may have seized due to thermal contraction so warming the area may help (soldering iron-careful yadayada...)
Some products (Japanese) use precision Phillips-type csrews that LOOK like standards, but you should get a good set of Japanese screw drivers if you do this regularly. Search the Humanoid Robot built from Japanese servos, sites for details and sources.
On boats, its not uncommon to use oils, tapping, wait a few DAYS and repeat...several times. In a couple weeks- YOU WIN!
Now THATS persistence!!