Soap and water and spray cleaners leave a film and dry out the wood. I would just wipe it off with plain water or vinegar and water solution. Then use a wood cleaner such as Murphy's furniture cleaner from time to time
as well as polishing it with something like lemon oil.
Do not use a wax polish. Wax will cause the problems you're describing. If you've used a wax based furniture polish remove it with Murphy's Soap and start over.
If the table has not been sealed with a urethane finish I'd clean it well and paint it with a urethane type product. Check with someone knowledgeable in wood finishes. Home Depot could help you.