The attacks were not authorized by the US Congress, so President Obama is acting on his own authority and violating the War Powers Act and the Constitution.
Without the Constitution, there is no law in the United States. It looks like President Obama might be positioning himself to become a military dictator (or others are placing him into that position).
Since there has been no extension of the War Powers Act, apparently the legal basis for President Obama's attacks is the "Authorization for the Use of Military Force". However, that is a unilateral transfer of Congress' sole authority to declare war and is therefore un-Constitutional.
All checks and balances in the United States have been circumvented.
Right now, legally, the President can be charged with murder for all kills in Syria. However, the American legal community refuses to do anything.