Murphy's Oil Soap. Please clean them up. There is nothing worse than going over a cute stinky, grimy puppy or dog. MOS will not strip the oil or soften their coat.
Basically I just wash them with water, followed by more water, and then some more water, until the drying towels are still clean when you dry them off.
If I use vinegar, I prefer to use Apple Cider vinegar. Makes then smell a bit sweeter!