Drill as a last resort. Get yourself an extraction tool from a cheap hardware store like Canadian Tire up here in the Republic of Kan-er-du. Prep it like RedCal suggests then put a couple drops of a penetrating oil on it. It should only be in there snug not gorilla torqued.
You take whatever type head it is screw driver....place some baking soda on top of stripped out screw.put on driver...add super glue to the top and in a few seconds the screw will be bonded to screw driver with the welded up baking soda superglue mix and then unscrew it.....crazy but baking soda and superglue react to make a hard weld ...use the super glue that fits application...from runny to thick superglue Wash
You take whatever type head it is screw driver....place some baking soda on top of stripped out screw.put on driver...add super glue to the top and in a few seconds the screw will be bonded to screw driver with the welded up baking soda superglue mix and then unscrew it.....crazy but baking soda and superglue react to make a hard weld ...use the super glue that fits application...from runny to thick superglue Wash