The oil that goes into your engine is 75-80% original “organic” base stock. The other 20-25% is a concoction of many different chemicals to make the oil perform as intended. These additives could not be classified as “organic” by your defintion.
So labelling any motor oil as organic is sort of a meaningless excercise. Used motor oil is classified as a “hazardous substance” to make sure it does not get into the ground water or food supply. In the Arctic this oil is often burned in special burners to provide heating and cooking energy. The little air pollution it causes there is preferred to getting it into the ground water and rivers.
The best use for old oil is to re-refine it. Many engines can use it, such as large marine engines and locomotives. Burning it it cement kilns is another option, but may need scrubbers in the stack.