Oil and heat, and more oil and heat good Captain! They are the enemy of stuck fasteners around the world. Enough oil and heat and you can move anything. An electric heat gun isn't bad. A propane torch is better and MAPP gas torch has superpowers (but won't melt the steel).
Yes PB Blaster, Silikroil, or another good penetrating oil applied to a heated nut, a time or two. Then grab that nut with QUALITY locking pliers (vise grips if you will).
In a worst case scenario you can indeed cut the nut off with a Dremel tool I've done it plenty of times. Just remember you're a surgeon in such a case and the cutting disc will cut the bolt, your engine cases, your knuckles, anything it touches. Once you crack the nut, that is to say "break the circle" in any one location, it will come off like butter.
Here's an axle nut I recently cut off a V-Strom motorcycle with a Dremel. In this case we knew the axle and the nut were junk (there was a recall on soft, non-heat-treated axles) so we didn't have to be careful to protect the bolt. But we could have almost as easily cut off the nut without hurting the axle bolt.