Start with something gentle, then go gradually more aggressive from there. A quick wipe with Vinylex or the Meguiar's vinyl care would be my first recommendation. Failing that, some gentle soap/water (easy on the water). Failing that, try Windex. Failing that, try Simple Green/Pro 409. You could also try some "goop" or "gojo" type cleaner. Once you have killed the stains retreat with Vinylex or Meguiars.

Hope this helps...Lee

PS be sure to use a terry or brush that has enough nap to get into the grain of the surface being worked on.