I've used a bath of diluted sulphuric acid for the bits from my Midas, an overnight soak will shift virtually all rust as long as the part has been degreased and is without paint. The parts are rinsed in water and then dipped in caustic soda to neutralise before being rinsed and dried. Alloy parts just need a fairly short time in the caustic to clean them up.
I haven't used vinegar, but I've heard of it being done and can't see why any acidic solution wouldn't work if given enough time. It's got to be the safer option if you've got kids about too.
Rich