(1) We did not go to war against "Libya" but we have taken action against the illegitimate dictator Muammar Gadaffi. We are allied with, not at war against, the Libyans who are calling for the restoration of the legitimate Libyan constitution.
(2) one does not need to be "obligated" to act in order to act. One need only be authorized or empowered.
(3) The part of the NATO treaties that carry that authorization are commonly called Berlin Plus.
No treaty can remove that power given to Congress under the Constitution.
What part of the “Berlin Plus” provisions cover our military actions (also know as war) in Libya?
And we are most certainly at war, via the clear meaning of language in the Constitution, with that segment of the Libyan population that supports Gadaffi.