Once you strip the head of a screw or bolt you are in the machinists world. Many of the tips in this thread work sometimes, especially all the vice grip ideas, but not all the time reliably.
Screw and bolt extraction begins prior to actually stripping the head. If there are signs of corrosion
or an unusally strong force is required it is always better to try a lubricant with a combination of heat prior to stripping the screw head.
Heat works well but application of the heat is gradual. It's nice to accentuate the different coefficients of expansion with a rapid temperature change. For this I like to heat up the bolt and the surrounding area with a torch. A pin torch helps in tight areas. Don't be shy - get plenty of heat into the bolt and the surrounding area. A color wax temperature pen can be helpful in determining the temperature if desired. Remember - you want the heat to penetrate down the bolt threaded shaft so you need to apply the heat for a while. You are usually assisted here because hardened bolts gernerally expand slower than any case materials.
Once the area is nice and hot apply ice directly to the head of the bolt and avoid the surrounding metal if possible. Another technique is to deluge the bolt head with ice water
applied through surgical tubing. The idea is to let the surrounding area stay hot while cooling
the bolt. You will have to keep applying water
until the bolt is cool.
After this you can heat a second time. When it is hot apply a pentrating oil
and tap the bolt head firmly. Wait 30 minutes or more applying the penetrant and tapping at intervals.
Then try the bolt again. This will almost always get the bolt out.
Part II - If you strip the bolt head.
Drill the appropriate size easy out hole. You should pick a size that leaves a very thin bolt wall thickness without risk of damaging threads. You should drill deeper than you think you need to go. And you must absolutely drill on center.
Then apply the penetrant methods above.
Then insert the easy out. You may need a second pair of hands but one pair puts pressure on the easy out and a second pair taps the head of the easy out with a drift and ball peen. You want to continue to shock the threads while applying torque.
Part III - What to do if you break the easy out
This should never happen but if it does there are easy out extractors (go figure?) Get the right tool for the job and remove the broken easy out.
Go back to part III - You probably didn't drill deep enough or big enough.
Part IV - I can't get the broken easy out out
Now you are in the realm of cutting tools, pin welding attachments and so on.
Probably the last thing that the backyard mechanic
can do is to get a dremel tool and cut the head off the bolt using tiny cutting wheels. Once the pump, flange or whatever is separated you can go back to work using easy outs. It is very tempting at this point to put a pair of vice grips on the nub sticking out.
I've done it, many times successfully. Sometimes not.
The very last resort is to drill out the bolt or stud and helicoil in some new threads.