If the metal really is aluminium then the only way to clean back to a smooth finish is as John indicates. Soaking and/or boiling in various chemicals will result in a certain amount of pitting where the weak spots in the layer of gunge are penetrated first. If that's the way you want to go, try cooking up some batches of real tomato sauce; the recipes are fairly acidic and the results taste great whatever the residual flavours were in the gunge you're trying to remove.

Polished aluminium surfaces don't stay bare for more than hour or so; the aluminium surface quickly oxidises (it still "looks" polished) and the oxide protects the metal underneath from further chemical action unless you get stuck into it with really alkaline or acidic chemicals, foodstuffs included.

Tests we did many years ago on aluminium billies seemed to support the notion that a polished outside surface gave the best heat transfer when using a choofer (gas, white spirit or kero stoves that burned with a blue and nonsooty flame) while blackened ones gave the best heat transfer over a campfire. But polished pots look better in a kitchen than blackened ones.

Cheers, Rowan