For me when my watch feel oily/dirty if the watches are water resistant/waterproof I wash with dishwasher liquid use toothbrush others no water resistant just wiped with a damp cloth that what I do.
I never service my watches until it not working.
Now there are six watched need repair most are vintage, it would be expensive, most of this watches cost 50 to 250 ringgit, if repair it would cost more than the price aI paid for and also good watch technician not easy to find.