Used instead of a grunt, when you don't know how to respond, when you drop something, when you see a relationship quote you can deeply relate to... etc.
*Drops phone on the ground* Oof. I hope I didn't break it. I didn't even get Samsung Premium Care on this thing.
Oof. The word Oof is generally used when someone else, or the user of the word, does something wrong and makes a mistake. The response is “Oof”. The word itself sounds like it would be used in an undesirable situation.