World War II (abbreviated WWII), or the Second World War, was a worldwide conflict which lasted from 1939 to 1945. Caused by the expansionist and hegemonic ambitions of Germany, Italy, and Japan and economic tensions between all major powers, World War II was a confluence of two conflicts respectively started in China (the Second Sino-Japanese War), and in Poland (the Invasion of Poland). This global conflict split a majority of the world's nations into two opposing camps: the Allies and the Axis. Spanning much of the globe, World War II resulted in the deaths of over 60 million people, making it the deadliest conflict in human history.
In November of 1940, German Chancellor Adolph Hitler acquired a powerful mystic weapon known as the Spear of Destiny. With it, he intended on manipulating its power to dominate all of Europe. A British officer named Smythe learned of Hitler's plans and informed American president, Franklin Delano Roosevelt. Roosevelt, pressured by Congress to maintain an isolationist stance, refused to openly involve the United States in England's war with Germany. Instead, he formed the Justice Society of America.
After the attack on Pearl Harbor, December 5, 1941, US President Franklin Delano Roosevelt gathered all available Mystery Men and asked them to unite for battling sabotage and similar at the home front during World War II. Their activities were limited to the home front so they could not fall under the influence of Adolph Hitler's Spear of Destiny.
The Squadron soon included also the members of the Justice Society of America (during war time also called the Justice Battalion), the Freedom Fighters and the Seven Soldiers of Victory. Later there was a sub group of younger heroes, dubbed the Young All-Stars, who also were part of the All-Star Squadron.
Official records state that Reich Chancellor Adolph Hitler and his new bride Eva Braun committed suicide in a hidden bunker in Berlin in April of 1945. This is erroneous however and the true incidents that took place on that day are known to but a few. During the Battle of Berlin, the Unknown Soldier was sent on a mission to stop a Nazi super-weapon - vampiric octopuses called "Nosferatu". On April 29, 1945, he infiltrated Hitler's bunker, killing him and assuming the dictator's identity in order to call off the weapon's deployment. He then made Hitler's death look like a suicide. 
With the death of Adolph Hitler, Berlin soon fell to Russian forces. Several U.S. units, including Easy Company, were still active during this time. On May 1st, 1945, only one day after Hitler's death, the time-displaced essence of Alec Holland, the Swamp Thing, took root in the body of a possible ancestor, Alexander Holland. Holland had been killed by enemy fire in Germany, but the Swamp Thing was able to reanimate his body and communicate with the soldiers of Easy Company. Together, they raided a slaughterhouse which was actually a front for one of Hitler's magus bunkers. The abattoir was run by the Transylvanian Nazi Anton Arcane. Arcane used this facility as a staging ground for his experiments in cellular reanimation and it was here that the very first Un-Men were conceived. A U.S. air strike decimated the facility and Arcane was believed killed when he was gored by a steer. Arcane survived however and would return years later to plague the Swamp Thing. 
Tales told under the Vertigo banner do not all take place within the same reality. Many of them even take place on New Earth. In one possible reality, a British detachment of soldiers known as the Rifle Brigade embarked upon a strange mission called "Operation: Bollock". Mission parameters for this venture involved finding the lost testicle of Adolph Hitler.  Whether the adventures of this Rifle Brigade takes place within New Earth continuity or its own separate continuity is unknown.
On Earth-X, World War II was a prolonged conflict that extended for decades. American President Franklin Delano Roosevelt passed away from a heart attack in 1944, leaving the country in such a state, that Nazi Germany was able to develop atomic weaponry. By this point, both countries were reluctant to use such destructive capabilities against the other for fear of retaliation that the conflict continued using conventional warfare. Adolph Hitler's Nazi war machine soon reached American shores and dominated the country. Members of the famed Blackhawk Squadron nobly gave their lives fighting the Axis powers.  American soldiers tried to fight back, but by this point Hitler's scientists had developed mind control technology that weakened the opposition's willpower. By the early 1970s, the flag of the Third Reich flew across the entire nation. Some proved to be immune to the effects of the mind control devices, and small resistance pockets began to form in various cities.
The history of World War II as it occurred in the WildStorm Universe is similar to how it took place in other realities. The grim member of the Authority known as the Midnighter once traveled back in time on a mission to assassinate Hitler when he was but a young officer. He failed in this endeavor, but left a distinct impression on the Austrian by kicking him savagely in the groin.
World War II was a major plot device in season one of the Wonder Woman live action television series. Operating from a "secret Nazi base" in Berlin, officers in the Third Reich conducted their affairs in an effort to undermine America's war effort. They established a vast network of spies and saboteurs who infiltrated America's military apparatus, targeting weapons factories, military bases and government offices. To combat the Nazi threat, the War Department established the Air Corps Intelligence Division under the command of General Philip Blankenship. Blankenship's top man was former Air Force major Steven Leonard Trevor. In the Spring of 1942, the Amazon princess Diana came to the United States on behalf of the people of Paradise Island and adopted the guise of Wonder Woman. She also adopted the mortal alias Diana Prince and joined the Air Corps Intelligence Division holding the rank of Yeoman 1st Class. As Wonder Woman, Diana fought many Nazi agents and was even held prisoner in a Nazi stronghold in Germany. She fought against scheming aristocrats such as the Baroness Paula von Gunther as well as athletic power houses like Fausta - the Nazi Wonder Woman. After the war Wonder Woman returned to Paradise Island where she remained for more than thirty years.
Issues in event are unknown.