Hi Sharlet! If they feel sticky I'm thinking it could be from grease. Try TSP.
Baking soda and hydrogen peroxide mixed into a paste. Scrub with a toothbrush. If it's really bad, a wood safe degreaser like GP66 or Fuller.
Citrus Magic cleaner & degreaser
Washing Up liquid kills grease - use with hot water and a sponge. Then wipe dry and buff.
There is a product called tsp. It will clean off just about anything. However, test it on a small area first to make sure it doesn't damage the finish. Also, use cleaning gloves to protect your hands