So why don't cars carry around pure oxygen? The problem is that oxygen is pretty bulky, even when you compress it, and an engine uses a LOT of oxygen. A gallon of gasoline weighs 6.2 pounds, so the engine needs 86.8 pounds of oxygen (6.2 x 14) per gallon of gasoline. Oxygen is a gas, so it is extremely light. One pound of oxygen fills 11.2 cubic feet of space, so a gallon of gasoline needs 972.16 cubic feet of oxygen to go with it. If your gas tank holds 20 gallons of gasoline, you would have to carry almost 20,000 cubic feet of oxygen with it! This is a lot of oxygen - so much that it would fill a 2,500 square foot house.
Even if you compress the oxygen to 3,000 psi (pounds per square inch), it will still take 100 cubic feet to store it. To put that into perspective, a standard scuba tank holds about 80 cubic feet of gas, so it would take 250 scuba tanks to hold all that oxygen.
Because oxygen is so bulky, what people use instead is nitrous oxide. In the engine, nitrous oxide turns into nitrogen and oxygen, and it's the oxygen that people are after. Nitrous oxide easily liquefies under pressure, so you can store a lot more of it in a bottle than you can gaseous oxygen, which does not liquefy. Even so, a typical system will supply only one to three minutes of nitrous to the engine. In the process, it adds about 100 horsepower to a typical big block engine. The biggest problem is that the extra gasoline that the nitrous allows in the cylinder increases pressure in the engine so much that it can do some real damage, unless the engine is designed to handle it. That would be the same problem you would have with an engine breathing pure oxygen -- it would have to be quite beefy to handle the load.