Use baking soda or powder laundry soap (borax), sprinkled on the oil spot and the concrete..let set awhile then sweep with a broom. It cleans and brightens up the concrete. You might have to repeat the oil spot a few more times. It cuts down on crawly bugs too. If close to grass use baking soda rather than soap, so there is a problem with it bothering the grass.
Try some Trisodium Phosphate (TSP) available at Your local Hardware Store. Not expensive.
Try some Dawn dishwashing detergent.
Go Jo works wonders on any grease stain.
How do I get rid of vegetable oil from concrete?