Those things are always a pain to reach. Do you have tools?
I think I'd start with some lubricant, letting it soak into the threads as much as possible. If you've got some WD-40 try that. If not, a light weight oil, like sewing machine oil or other household oil. Then, clamp a pair of vice grips on the nut. You might then be able to turn the screw.
Worst case, you might have to "damage" the plastic nuts to the point where they crack and break. One possible way to do this is to CAREFULLY use a hammer and sharp chisel. Make sure you don't hit the porcelain.
Good luck.

use a hacksaw blade and cut off the seat bolts from the top of the rim. If there rusted they should cut off easy. never use a hammer anyplace near a toilet, hitting the nut with the chisel and hammer could break it.