Removing long-term residue from teflon
You cannot use physical methods (scratching), so you are only left with the chemical ones. And for this kind of gunk, the only thing I know to work is a strong enough base.
In the mildest cases, oven cleaner sprays might be sufficient. If not, somebody suggested ammonia in the comments, and then there is lye.
The big problem is that any base strong enough to clean this stuff will corrode aluminum too. If your pans are teflon on steel, go ahead and clean them. If they are aluminum pans, maybe you can try the oven cleaner as a last ditch effort, but you are risking the pan itself. Else, all you can do is continue use them as normal sticky pans.
The usual modus operandi is actually not to clean them somehow, but not to let the gunk happen. Just like you don't use metal on Termin, to prevent the failure mode of &quot;scratched pan&quot;, you don't use techniques which produce gunk, to prevent the failure mode of &quot;gummed up pan&quot;. This means that you have to avoid anything with small amounts of oil, and either use the pan without oil (at low temperatures though, or you'll burn the coating), or with lots of oil at moderate temperatures, or for wet cooking.