"It has been nearly 60 years since the last declaration of war by the United States." True. The Korean war was action of the United Nations, and the United States forces involved in this war were operating under the aegis of the U. N. Therefore, presumably, a declaration of war from the United States was not legally required.

"Have all of the wars since then been illegal?" Other than the aforementioned, whether you like it or not, according to international law, yes, they were illegal. International law requires that a state of war be declared twenty-four hours before the commencement of hostilities. The last time war was officially declared by the United States was during Frenklin D. Roosevelt's "day that will live in infamy" speech on December 8th, 1941, when he declared that a state of war now existed between the United States and the nations of Japan and Germany. This, of course, in response to the sneak attack on Pearl Harbor on the previous day.