First...Try using a phillips head slightly larger than normal for that size screw. Not too larage. The tip of the phillips head must still fit in what remains of the screw hole.
Second thing if that does not work.......Can you get hold of the sides of the screw head with a pair of pliers? If so, use a pair of locking pliers (vise-grips, etc); lock the pliers tightly around the screw head; and twist the pliers (and the screws) off. Needle nose vise-grips for tight places best.
Second thing if that does not work.......Can you get hold of the sides of the screw head with a pair of pliers? If so, use a pair of locking pliers (vise-grips, etc); lock the pliers tightly around the screw head; and twist the pliers (and the screws) off. Needle nose vise-grips for tight places best.