When you look at all of the work we do to go fast, it's all about getting more air in the engine. We deal with an air limited sport. You can dump fuel in with a fire hose.
The SCTA splits the world into three parts.
1. Gasoline.
2. Every other approved liquid fuel; alcohol, hydrogen, nitromethane, and unapproved gasoline. Nitrous Oxide also, but it is a special case. There are thousands of combustible compounds, these are the approved ones.
3. Supercharger or turbocharger. (Gas or fuel)
With gasoline you are limited to the amount of air you can stuff into the engine. Physics dictates that a 14.7:1 ratio of gasoline to air is the stochiometric ratio where all of the fuel will combine with all of the oxygen. That's 14.7 pounds of air to 1 pound fuel. The air we breathe is 21% oxygen, 78% nitrogen and other trace gases. The oxygen is the only thing that matters. Above or below that ratio and you will be rich or lean and produce less heat to expand and drive the piston down. Because it is a dynamic event, and not in a laboratory, a ratio of 12.5:1 to 12.8:1 is the rough ratio for maximum power depending on the blend of gasoline used. At 14.7:1 you will produce roughly 18,400 btus of heat per pound of fuel.
Switching to the fuel class and running methanol results in 9,500 btus per pound of fuel. Far less! If you burn methanol in a coffee can in the sun light you can't see the flames. So why is it a better fuel? Because it combines better with oxygen. At 5:1 ratio you can stuff twice as much in the cylinder and achive 20% more power. Methanol has a higher heat of vaporization than gasoline, so that as the liquid fuel changes to a vapor, it cools the engine more than gasoline.
Putting in nitromethane results in only 5000 btus per pound of fuel. Even less! The chemical formula is CH3NO2. Notice the two oxygen molecules? Nitromethane is a monopropellent by itself. You can pour a massive amount of nitromethane through an engine due to the 1.7:1 fuel/air ratio. The result is 135% more power than on gasoline. IF the engine will take it. It's no wonder the top fuel guys use it. The higher heat of vaporization combined with the higher fuel flow results in a lot of engine cooling.
Which brings us to nitrous oxide. SCTA classifies it as a fuel, although it is an oxidizer, not a fuel. When you squirt nitrous into an engine you displace the 21% oxygen air with 33% oxygen nitrous. Everything noted above for the fuels increases because you can dump more fuel because of the increased oxygen. The breakdown of the liquid nitrous oxide into N2 gas during combustion releases heat separate from the oxygen benefits, adding more power. Can you run 100% nitrous oxide with no outside air? It would depend on the size of the engine and how many bottles you can carry. It's more to the point to ask the question "At what point will it grenade?"
A supercharger or turbocharger allows you to stuff more air in the same volume, allowing you to put more fuel in for a bigger bang. Can you use nitrous oxide with a supercharger or turbocharger? Sure!
Can you achieve a supercharging effect with nitrous oxide alone? With a direct port injection you certainly can! Nitrous oxide is popular because it's easy. Nitromethane is looked at as only something an "expert" would use. The true answer is in the fuel class there is no end to the power you can generate, probably far more than the engine will take. In the supercharger or turbocharger classes destroying an engine is not hard. So, crank up the boost or tip the can until it blows, then back off a little.