Rinse the oily rags under cold running water for several seconds. The water will help rinse the oily residue out.
Set the washing machine to a normal wash cycle with hot water. Add a 1/4 cup of laundry detergent either in the washing machine drum, or in the detergent receptacle.
Pour one cup of white vinegar directly in the water-filled washing drum. The white vinegar will cut through grease, oil and grime, while removing any trapped odors in the closed loop rags.
Submerge the rags in the washing machine and close the lid. Allow the washing machine to complete the wash, rinse and spin cycles.
Remove the rags and tumble dry on low heat or air dry the rags.