I've been in a situation like this before. It can be frustrating and annoying and if you let that get to you, you may cause more damage. Best advice I got:
"It's only metal. It'll yield."
Counterintuitive, I know, but rest assured you can fix this problem. Here's what I would do.
1) Chemical Warfare. Start spraying them down with Jig-A-Loo or some other penetrating oil of your choice. Spray them today, tomorrow, and the next day until you can seriously tackle the fasteners and let the oil do its' thing. I suggest spraying and then giving the fasteners a light love-tap with a hammer to encourage the oil to seep up the threads.
2) While your penetrating oil is doing it's thing, you've got a few options to engage in the mechanical removal of these fasteners.
If there is any part of the fastener showing, you can try to get a vice grip on them and twist them out.
If there isn't any fastener showing you need to get a bit more aggressive. I'll list a few strategies to try, but be warned if one fails it may make some of the others more difficult so weigh the options before committing.
- You can try to cut a slot in the fastener using a grinder. This might be enough to get a flat screwdriver and turn them out. This will likely fail if they are rusty.
- If you have a welder, you can spot-weld a good fastener on there and try to remove it by getting a wrench on that. This is more likely to work than the cutting of a slot, but beware that the heat can mess up the threads so be careful and don't really give it with the welder.
- If you can't weld it you may need to drill it out and tap it. For this, go buy yourself some left-hand turn drill bits -- you'll only need a little one for a pilot hole, and one that is just slightly smaller than the fastener. They are available at any decent machinist supply place. The left hand turn drill bits go in a normal drill but to drill 'in' to the material you put you drill in reverse. This way, there's always a chance that the drill bit will catch the fastener and spin it out as you drill it.
Before you drill the fastener, make sure you can get a good pilot hole. Use a punch and mark the center of the fastener and be VERY straight. Fasteners are often very hard and it's easy for a bit to wander off into the material the threads are in. This is fixable, but it's a pain.
You may be able to drill it out and run a tap of the appropriate size through the threads to clean them, and bob's your uncle. However, if you can't do that, you may need to drill the whole bigger to remove all the fastener and the old threads, and then re-tap at a larger size. This should be a last resort as it's a pain in the butt to have one odd-sized bolt on the whole machine.
Now: If all of the above fails, and you need to repair the whole from scratch, you have a few options. You can secure a bit of metal rod into the hole using a high-strength reinforced Epoxy. I'd suggest something like Devcon Titanium. I've fixed an aluminum block on a motorcycle with this stuff and it's amazing -- it's just a few PSI of strength shy of the aluminum it's surrounded by. Then you basically start from scratch -- drill a new hole and tap it for the bolt.
Before you try ANY extraction, and after you've soaked the fastener in penetrating oil, try to use physics as much as is safe to your advantage. Try to heat the metal the fastener is bolted into; this will cause that toe expand. Bonus points if you can simultaneously cool the fastener itself, which you can do using a spray can of this stuff:
http://www.loctite.com.au/3320_AUE_HTML.htm?nodeid=8802649931777
That'l help break free the fastener.
Hopefully this will give you some options. This stuff is all fixable, just keep a cool head and be strategic. Feel free to post back how you get on or if you need me to expand on the above.
(P.S. I know you could also get an induction coil thing, but those cost $$$$$ so that's why I left it out)