Not quite.

>Well, **I'm off**!

Means that you're **leaving**. See: [TheFreeDictionary - I'm off][1].

>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?][2]

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.


  [1]: http://idioms.thefreedictionary.com/I'm+off
  [2]: https://english.stackexchange.com/questions/84659/what-does-the-idiom-to-sound-a-little-off-mean