Bar keepers friend and a little bit of elbow grease should get it all off.

A LOT of elbow grease and BKF! I heated oil in a new All Clad skillet to make pancakes and the oil cooked onto the side of the pan. It took at least 20 minutes and several damp paper towels to get out every trace of it.

Stainless Steel does not "season", that only refers to cast iron. Just delegate the old pan to popcorn only and buy a new pan that is never used for popcorn.

BKF works just OK, but for really tough polylmerized oil, try Dawn Power Dissolver. Demeyere makes a special cleaner with mild acid and grease cutters that also does a good job. Some people resort to Easy Off in the oven, but I've never had to try that.

Thanks everyone! BKF actually did just fine. I boiled some water with dish soap in it, then dumped that out and scrubbed with some steel wool and the BKF. Came right off! My pan looks nearly new :)