Hi Im new to this website and i have really been struggling with this problem. I have an old 27 inch Schwinn road bike that im trying to restore and the rear wheel's nut has been worn to the point where i cant take it off. I tried to take it off , but the problem seems to be getting worse . there is practically no grip or sides left to the nut and i NEED to get it off in order the replace a few things on the rear wheel ,
First give it a good overnight soaking with a penetrating oil, than grab it with a pair of vise grips and take it off counter clockwise. Large pair of pliers with the center grabbing notch may work too. Get a new nut......
Never Give Up!!!
I had to get a hacksaw to a brake bolt which was jammed on once, have to be very careful with the shavings getting into unwanted places and even more careful with where the saw goes, a very last resort and you've got to be very tactical with where you cut!