The ultimate way to remove burnt-on stuff from aluminium is a motorised wire brush. Solid brass is fairly aggressive but manageable (watch out for brass-plated steel, which is too hard). Sets are available with nylon and brass brushes in various shapes to mount in a drill. Brass will scratch up the surface, but you can polish the worst of the scratches out with abrasive cleaner if you really want to.
Before that it might be worth trying the most aggressive kitchen degreaser you can find, sprayed on, left for a few minutes, then scrubbed with a nylon scouring pad. One I've used does slightly soften burnt-on grease, though it doesn't dissolve it.
The manufacturers Bar Keeper's Friend recommend it for use on aluminium, including for burnt-on oil, but I haven't tested it myself.
The degreasers to avoid are the strong alkaline solutions