Wash the oily stain with a clean cloth and a commercial degreasing cleaner. Alternatively, combine equal parts hot water and vinegar to create a degreaser. Vinegar cuts through most oil and grease.
Inspect the wall for any remaining oil marks after the surface dries completely. If marks remain, the oil likely soaked into the paint and cannot be washed off.
Paint over the oily mark with a quality primer. Use a latex primer for walls painted with latex paint and an oil primer for those painted with an oil paint. Usually, latex is used on drywall, and oil is used on wood walls.
Allow the primer to dry completely, typically for at least four hours. Inspect the area to ensure the oily mark has not bled through the primer. If it is still visible, apply a second coat of primer and allow it to dry.
Apply a fresh coat of paint once the primer dries completely. Paint between one and three coats of the final color so the repaired area matches the rest of the wall.