You should be able to unscrew the whole stem and just replace without cutting anything. You're not sweating in a new valve.

But otherwise on removing a screw, left hand drill bits (so it grinds in while screwing it out), cutting a slot so you can use a flat head screwdriver, maybe even just vise grips are good techniques.

I would soak it in something like PB Blaster or AeroKroil (just be aware these things can stink and linger, especially PB Blaster)