Nut splitter, dremel, rotary cutter, drill and hammer and chisel are probably your best bets.

The lesson here is not to use aluminum wheel nuts. The weight savings are negligable for a street car and the potential downside is a big PITA.

In hind sight, you probably should have used a very deep throat socket to grip the whole nut, but you probably figured that out by now.

If you can't split the nut, or put a notch in it, stick in a chisel or screwdriver, and hammer it out, you are gonna have to drill out the stud.

I don't envy your predicament.

 

i bought lightweight nuts at ebay and after i received them they were so soft that i could chip hte with a knive......
what a crap

i returned them and it turned out that for stock wheels ball seat nuts are a must and not a conical ones.