OK, didn't know the springs were not making contact. In that case thats one task you don't have to deal with. All the rest of previous advise I still suggest.
If corrosion is what is keeping the nuts from turning you need some good penetrant and the correct tools for turning the nut. Don't be afraid to try to move the nut in both directions just to break the corrosion loose.If the nuts somehow got cross threaded you are going to have a bigger job than you may want to deal with. It would involve cutting the nut off with a small die grinder. Then you would have to try to repair the treads with a thread chaser if they are damaged. Then finding a replacement nut. All this I would not try to accomplish while the strut is still on the car.