My method.
First attack is always to soak with penetrating oil then go have a beer and cone back the next day.
Second wave; grind any exposed surface flat using a dremel or die grinder, using a sharp punch held at an angle and a small ball pean hammer try to tap the screw/bolt out.
If the second wave initially fails apply heat to the surrounding metal and try again.
Third wave; if the above fails use the dremel/die grinder to create a divot in the center of the screw/bolt. Drill a small hole down the center of the offending hardware, a regular drill works fine for this and is much more likely to be in your shop that the left hand variety. Repeat the penetrating oil application, heat, punch steps.
Fourth wave; repeat the drilling process with the next size up drill bit.
Repeat as required, at some point you will either succeed, remove enough of the fastener to clean up the threads with a tap, or destroy the threads in the hole.