Is there a secret to the successful use of Murphy's oil soap? [View all]

I have old pine kitchen cabinets. Every so often I feel the need to wash them down. They are stained and finished with Minwax poly. Here and there there a a few nicks that I must touch up.

I tried to clean them a short time ago with Murphy's and found that the product did not seen to remove shadows of spots(spatters) on the wood, especially above my stove. I'd like to find something that would remove these spots that does not say "do not use on" whatever.

Do you have any ideas?