Tea tree oil cuts through this kind of crud with no trouble at all 

  Just daub a bit onto a cloth and wipe.  Follow up with a quick scrub using your favourite old toothbrush and some warm water + detergent.  Dry throughly before re-assembling.
Seriously, just last night I used tea tree oil to clean a set of disgustingly filthy buttons from an old cab.  At first I thought I had a terrible job ahead of me, but it turned out to be no problem at all with the tea-tree oil.
A bottle of tea-tree oil costs about $2 at the supermarket in Australia, maybe $4 elsewhere I guess.  Also makes a fantastic disinfectant and mosquito repellent.