ShaneRidesBikes,

For better or worse, that nut has to come off. There is nothing that is going to just "miracle" it off. Clearly, you are suffering from either a cross threading or more probably (if you tried both nuts) wrong size threads on the nut. If the axle isn't damaged (too much) after removing the nut just take it with you to the hardware store and either try nuts yourself or if you are lucky some guru in the store will measure the threads for you and get you proper washers and nuts.

Given that your original nuts were stripping and one of the new ones are stuck I would like to respectfully suggest being a little less ham fisted with your bike. Trust me, that comes from a fellow ham fist. Work slow, trust nothing that doesn't go on smooth as butter and grease everything as you go. Everything. While you are at the hardware store pick up a tub-o-marine grease. They should have it. If not, a tub-o-regular grease will do great. While chains are an exception (and possibly hubs) nothing else will benefit from over priced, bicycle specific grease. Nothing wrong with the stuff of course. But, it is ridiculously priced. That said, a few years ago I picked up a tub of Finish Line Teflon grease on fire sale and use it on my hubs and pedals. It seems to work great. Still have a bunch left.