Not quite.
Well, I'm off!
Means that you're leaving. See: TheFreeDictionary - I'm off.
This song sounds/feels a little off.
Means that there is something not quite right about this song to you. It feels weird. A thread on ELU about that: What does the idiom “to sound a little off” mean?What does the idiom “to sound a little off” mean?
If you wanna say you're not feeling well, you could say:
I'm feeling a bit under the weather, I think I'm going to go home.