The are only two "war powers" in the Constitution:
That's it. Congress can declare war, and Congress can approve states engaging in war.
The President, as Commander-in-Chief, has Article II Section 2 plenary powers to use the military as he wishes. He doesn't need the permission of Congress, or else we'd have a Congress-in-Chief where the President becomes a lesser officer.
Congress can declare war, but that doesn't obligate the Commander-in-Chief to wage that war, either. The President could choose to use diplomacy to de-escalate tensions and never act on Congress' declaration of war.
The Article I Section 8 power of Congress to "declare war" is not a check on the President's power to use the military. The proper check is the Article I Section 8 Clause 12 power:
To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
The power of Congress to defund the army was the check on an adventurous President who is misusing the military. A president has a two-year window to use the military before Congress must reauthorize the funding for the military for another two years.
That is how Congress oversees the president's use of military power.
-PJ
Thanks for pointing that out. Every president has considered it unconstitutional. If the senate pushes it, maybe we have a man that will push back.