Oxygen is mostly used in applications which require intense heat because it promotes burning. Funnily enough, beyond that it is more of a nuisance than a help.
In fact, from an engineering point of view, Oxygen is quite nasty stuff to have around. If breathed under much more than atmospheric pressure, it is poisonous. It corrodes iron, steel and aluminium and causes oil to spontaneously burst into flames.
For these reasons very little oxygen is used in aircraft in pure form. About the only application is in emergency bottles used if we have someone becoming ill on the flight.
The emergency oxygen system actually relies on oxygen being released in a chemical reaction, the oxygen itself is chemically bonded and inert until the reaction takes place. Otherwise it could cause a fire.
Divers don't usually use oxygen, they use compressed air which contains oxygen, otherwise it is toxic.
The only real application you mention is in welding, and even then, for some metals you have to use the oxygen to fire the flame, but stop it getting to the metal.
As I said, from an engineering point of view, nasty stuff. But it is a bit hard to live without it!