Under USA law, is the president allowed to take the nation to war? No. The US Constitution allows only for the Congress to make war.
US Constitution, Article 1, Section 8:
The Congress shall have power to...
To declare war, grant letters of marque and reprisal, and make rules concerning captures on land and water;
There is of course the USA's War Powers Act, which further defines who can do what in times of war. However, the War Powers Act also states:
Nothing in this joint resolution--
(1) is intended to alter the constitutional authority of the Congress or of the President, or the provision of existing treaties; or
(2) shall be construed as granting any authority to the President with respect to the introduction of United States Armed Forces into hostilities or into situations wherein involvement in hostilities is clearly indicated by the circumstances which authority he would not have had in the absence of this joint resolution.
What about internaional law? One law of particular interest which the USA signed on for is the United Nations Charter, which states:
United Nations Charter, Chapter 1, Article 2:
Part 1: "The Organization is based on the principle of the sovereign equality of all its Members."
Part 3: "All Members shall settle their international disputes by peaceful means in such a manner that international peace and security, and justice, are not endangered."
Part 4: "All Members shall refrain in their international relations from the threat or use of force against the territorial integrity or political independence of any state, or in any other manner inconsistent with the Purposes of the United Nations."
http://www.un.org/aboutun/charter/
There is of course Chapter 7, but that is irrelevant since the SC did not make any such decision.
An interesting website:
http://www.lawyersagainstthewar.org/ Obviously these people have a stated bias, but the law is written in black and white.