Sounds like you might be using too much oil.
Another thing, especially if you use vintage stones, they often come in wooden boxes. So no oil should be making it's way to the table during use, and the box should prevent contamination, though I keep my stones that don't have boxes in felt sleeves to keep them clean and free of dust, etc.
If all that seems like too much maybe look at the shapton glass stones. They work well and are splash and go.
