I assume that the Mute option is NOT checked in System Preferences, Sound, Output. Sometimes the descriptions of toggle switches can get confusing.
Have you tried turning it on (mute) and then trying the sound keys? Maybe, it's reversed itself? Or, try an on and then off?
Have you tried holding down the fn, function key, while pressing volume keys — i.e., F10, F11, F12? It could be that an option under Keyboard, Keyboard, i.e., Use F1, F2, etc. as function keys is checked ON when it should be off!
Have you restarted the computer?
IIRC, one of those PRAM or NVRAM resetting key combos is supposed to handle and restore sound, too. So, that's another option to try. You may end up having to manually restore some settings afterwards (time, network, etc.), but it,d be worth it to get your sound back.