The first thing you need to do is get your nomenclature correct so your problem is correctly understood. Though not technically correct*, the following terms are in general use.
A screw is a fastener you use a screwdriver to turn, usually flat or phillips, and more and more, Torx.
A bolt has a hex head that you use a wrench or a socket to turn.
A nut is hex shaped with internal threads that threads on the end of a bolt.
There are variants on all of course but using these general terms allows us to know what your talking about. I'm assuming you mean that there's a bolt that's threaded into the swingarm that pushes against some sort of block on the rear axle. There is a nut that locks the bolt in place, and that the hex sides of the nut are stripped, not the threads. If this is the case, the first thing to do is spray it with a good penetrating oil. Kroil is generally accepted as the best, followed by PB Blaster. Pull the rear wheel and axle to get it out of the way. Put a wrench or socket on the adjuster bolt and try to loosen it (turn CCW looking at the head). If you're lucky the lock nut will break loose when you do. Don't get carried away and break the bolt. If a moderate amount of force doesn't break things loose, stop. If there's not enough room for vise grips, you should be able to use a hammer and chisel or (cringe) a screwdriver to hit it off center on the side(if it's the right side and the bolt head is to the rear, you'd hit the top side of the nut) and break it loose. If it's really stubborn, repeated heating and shock cooling (dump water on it) will help to break it loose. If you still can't get it, it's best to take it to someone with the tools and experience to do the job without causing further damage. Once you get it off, simply replace the nut. I believe they usually use flange nuts which would be difficult to find locally. A normal hex nut with a washer would be a good substitute.
Marc -
*Technically what we commonly refer to as a bolt is actually a cap screw. A true bolt is not meant to be turned so does not have a head. Carriage and elevator bolts are examples of true bolts. Also, smaller sized screws (6-32, 8-32, etc.) are often referred to as machine screws. This is also incorrect. A machine screw is simply a screw that's fully threaded.