Sprinkle the oil stain with cornstarch to absorb any excess oil. Let it sit for a few minutes, then shake the cornstarch off.
Apply a few drops of grease-fighting dish soap to the stain. Let it sit for a few minutes. Blot excess soap with a clean paper towel.
Wash the dish cloth in a washing machine. Check the manufacturer's directions for washing your cloth and use a hot water setting if possible.