what i would recommend is taking it apart, removing all the electronics, and just hosing it heavily with rubbing alcohol. the stuff is cheap enough, you can get big bottles at drug stores for a few dollars. put some in a spray bottle, spray into all the crevices/gears/etc, pour a bunch in a container and submerge it for a while, whatever helps you clean it out. that should dissolve the sticky crap and get it off there.
the reason i say to use rubbing alcohol instead of water is that rubbing alcohol evaporates a lot better by itself, so you don't risk rusting any steel parts as much. after you are done cleaning it, you should dry it off as best you can. preferably take an air compressor or some of that "canned air" people use to blow dust out of their computers, and make sure you get it totally dry, and you should probably also let it air-dry for a couple of days in a warm, dry location (by a hot air duct or other heater in your house, or something like that) so you are sure there is no moisture left.
it would be a good idea to oil the gears and things once dry, you can get multi-purpose machine oil at any hardware store. that will help things run smoothly (in case you washed out the original lubrication) and also help prevent rusting.
you could also do this with a different, more volatile liquid, like mineral spirits or acetone or something. they would probably do an even better job of cleaning out the gunk, and evaporate even faster so rusting wouldn't really be an issue, but they would cost more, have more fumes, and could possibly react with some plastics in there...