[Joeaksa]

First thought if you do not have access to a good socket set (snap on or the like) is to find a Discount Tire store. Find a tire store who is good at what they do and get them to loosen the nut before whats left on the wheel is rounded off. A good tire store works with taking wheels off all day long and may be able to get it off.

If you have access to a good socket, like a snap on deep socket, then I would very carefully try to loosen what little is left of the lug nut by having one person push on the socket to keep it level and on the nut and another person applying pressure trying to loosen the nut. Might use a small torch or heat source and warm up the lug nut to try to get it to expand a bit before trying to do this. Downside is that heating the aluminum is not going to make it any stronger so would be very careful with this.

If it just rounds off then my gut is that you will end up drilling one or two small holes in the lug nut to cut it in half and then taking the pieces out. It would have to be done very carefully to keep from damaging the wheel.

Never seen this happen to a lug nut... makes me wonder if someone has used a air wrench on the car before?

Joe