Vinegar is a weak acid. It won't touch your stains but will leave an unpleasant odor everywhere.
Try Super Clean, a strong, water soluble cleaner. It is available at Wal-Mart.
Careful, wear gloves if you're going to handle the wet parts...undiluted, the stuff will remove skin. Also, keep it away from glass...it can etch glass if not removed promptly.
It contains NaOH (sodium hydroxide) and silicates (strong alkalies). The pH is about 13.
I use it for grease removal on metal parts, carburetors, cleaning plastic furniture, as a deck cleaner with the pressure washer (diluted), carpet stain remover, laundry pre-spotter, cleaning the bar-b-q smoker, cleaning concrete, cleaning the wife's gold and platinum diamond rings, etc.
Diluted, it is excellent at cleaning auto wheels, tires or white walls (remember those?).
If the stains you have are cooked on oil, this stuff will take it off.
Oh, and its cheap....~$10.00/gallon. I purchased my last gallon about two years ago and still have plenty left.
Super Clean is my regular go-to all-purpose cleaner. I have it around in spray bottles at various strengths.