What proportion of a combustion engine's output energy comes from the air?
In combustion the "energy" is really the heat that is released. This heat causes the expansion that moves the piston upwards.

However, the fuel and the oxygen did not enter the engine with energy, and then leave without it. The fuel and the oxygen did not leave at all, different molecules did. The heat that was released was due to the reaction that changed the molecules into different molecules, it was not "brought" and handed off by the molecules. I don't think you can divvy this energy up, since it would not have happened without either the fuel or the oxygen. 0% of the reaction would have happened without the oxygen, but that doesn't mean the oxygen was responsible for 100% of the heat generated.

If the oxygen had entered at one temperature, and left at another, you could calculate the heat the oxygen released or absorbed by its change in enthalpy. However, this does not happen in combustion, the oxygen that is responsible for the reaction does not leave as oxygen.

In fact, if anything, the uncombusted oxygen absorbs heat that could otherwise have been used in the expansion of the piston and this quantity would be measurable. So the only thing I think you can quantify is the amount of work not done because air is used (same goes for all the nitrogen that goes in cold and leaves hot). If pure oxygen was used rather than air, engines would get more expansion work since less heat would be absorbed by  nitrogen.