Pour a thin layer of cornstarch or talcum powder on the stains to absorb any oil. Let the powder set on the stains for two to three hours.
Vacuum up all the powder using a wet/dry vacuum or one with a brush attachment.
Scrub the stains with a fine-grit sandpaper by rubbing the areas in a circular motion. Do not scrub down too far to prevent damage to the fabric. For small areas, rub with a pink eraser instead. Allow wet stains to completely dry before sanding them, and scrub the areas in a circular motion with a stiff scrub brush.
Clean the stains with a professional suede cleaner if they still remain on the couch. Spray the areas evenly with the cleaner, and scrub them in a circular motion using a medium-bristle scrub brush.