Eagle One A - Z wheel and tire cleaner will do a better job than any of the ideas above, and over the years I have tried every suggestion listed in this link at one time or another. A -Z when used aggressively is just a great product, the brown dirty crap will just run out of the whitewalls in a few seconds after you soak them, take a medium bristle brush to the them after letting them soak about a minute and then rinse. Very good product. But I will say a lot of good suggestions in this link, except the lacquer thinner one, thinner WILL detoriate the tire or anything else rubber if enough is used, and is very bad for the paint in the area if you are not awfully careful.
IMHO