They are like ball joints. The ball joints can swivel when you turn the nut also. I would suggest to wedge a pry bar in between the sway bar and the links,and then put presure between the two. That should hold the bolt tight enough to spin the nut off. You could also put a closed end wrench on the nut and then grab the bolt with a vice grip and turn it. If all else fails, maybe try to get a hack saw in between the link and the sway bar and cut it off. something like this is the best:
http://www.designbuildlisten.com/ezshop/433821asml.JPG
They are cheap too. Hope that helps.