Open all of the basement's windows and doors, and place a few fans in the basement to help ventilate the area.
Mix 1 gallon of hot water, 1 cup of white vinegar and 4 oz. of vanilla extract. Use this solution to clean the basement. Clean every surface in the basement. Vinegar is a strong odor eliminator, while the vanilla extract adds a pleasant scent back into the air.
Open several boxes of baking soda and set them on chairs. Place the chairs in various spots around your basement. Baking soda absorbs strong odors, such as oil odors.
Fill 10 bowls with ground coffee and set them around the basement. Put these directly on the basement floor to absorb oil odors low to the ground.
Repeat every couple of days until you no longer notice any oil smells.