A formal declaration of war as some document that stands on its own entitled, Formal Declaration of War, has never been necessary nor constitutionally required. It was a practice already out of practice when the Constitution was written and Hamilton discusses that in The Federalist Papers. Congress enabling the executive to use force or ordering him to do so is all that is required. In that, the war we are currently fighting was in fact legally enabled by Congress through authorizing law.
I thought that, legally speaking, we were at war during World War II because we declared war on December 8, 1941. Since there were no declarations of war for Korea, Vietnam, Iraq, or Afghanistan, none of those conflicts are wars in legal terms. (Neither was the Civil War; that was a police action as well.) Is this correct?
No, it's not correct.The Korean War was a UN action. The initial military involvment of the United States was under the guise of the UN Charter. However, Truman eventually did go to Congress and was authorized to use military force The Vietnam War started in a similar fashion with Congress eventually approving the use of military force. The authorizing resolution for Iraq and Afghanistan is likely the same one published as Public Law 107-40 :
That the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons, in order to prevent any future acts of international terrorism against the United States by such nations, organizations or persons.
That same authorization also codifies the War Powers Act language necessary to give the President the authorization.
Any one of these acts is all the Executive needs under the Constitution. We may call different military engagements different names for political expediency (and we do) using such phrases as war, police action, invasion, supply support, etc etc. But in the end, all the Constitution requires is Congress to approve the use of force. No matter what you want to title those authorizations, they are declarations of war for Constitutional purposes.