It is unfortunate, but the more powerful the country, the less likely the leaders of that country are to face international charges when they do something illegal. The US has a long history of illegally interfering with and attacking other nations and getting away with it because of amount of money and power backing the US. An attack on Syria would be no different, Obama would never be tried as a war criminal because the power of the US would shield him.
Even though the United Nations purports to act for all countries, it is actually heavily influenced by the United States, and indeed the US is in New York City. Because of the US's out sized role, Obama would not be a war criminal. Even then, international law is a creation of binding treaties, rather than a sovereign entity, as the UN is not sovereign.