How can I undo the tarnish on my aluminium headphones?
I would try any sort of weak acid that wouldn't cause damage to other parts of the headphones.

Citric Acid (found in lemon juice), Acetic Acid (found in vinegar), and Phosphoric Acid (found in cola) are probably all safe bets for sticking on a cloth and wiping off the casing. The primary difficulty you have here is the issue that comes from the fact submerging your headphones in anything would likely damage the electronics inside. You can rig up a shallow flat pan full of acid and resting the headphones on it's side in there, though I'd take caution.