Why were the Japanese so successful in the early years (1937–1942) of the war against a variety of Asian, European, and American powers?

The Japanese were successful because they devoted so much attention and money to their military. Their investments in air and naval technology paid huge dividends against the colonial and local forces across Asia. They had air power that was revered as the best in the world, a strong navy with the most advanced ships and carriers, well-trained troops, and motivation to fight for their emperor derived from a nationalist culture that believed in Japanese superiority.
They had brilliant strategists among their general staff, like Admiral Isoroku Yamamoto, who understood the need to take control of the resources across Asia which were largely occupied by Chinese, British, Australian, and American forces. They saw weaknesses with each opponent. The British were vulnerable because the majority of their forces were dealing with the Germans. The Chinese had a huge country to defend and not as modern of an arsenal to do it with. The Americans underestimated the threat they were facing: they thought taking economic steps against the Japanese would be enough to stop them. The Japanese were hungry to prove to the Americans, in particular, that they should be considered the dominant Pacific power. Their swift defeat of the Koreans and invasion of China did raise some eyebrows, but they continued to be underestimated. While they had their failures in the Soviet-Japanese border conflict and struggled for a while conquering China outside of Manchuria, they did not let those setbacks stop them.
The Japanese army became more seasoned as time went by. By 1939, when Europe was just getting started, they had been fighting longer than any of the other major powers. They were able to sign a truce with the Soviets and ally themselves with the Germans. The German puppet state of Vichy, France gave the Japanese military control of Indochina and all its resources. Controlling Indochina cut off one of the most important Chinese supply routes, putting the largest Chinese enemy in a fight for survival.
The Japanese took advantage of a largely isolated British colonial force in Malaysia, Java, the Andaman Islands, and Burma. They brought the full force of the Japanese military down and forced the British into their biggest surrender in history by capturing 80,000 men at Singapore. The remaining British and Australian forces were on their heels trying to defend India and Australia.
The plan to deal with the Americans was to knock them out quickly so they'd sue for peace. They hoped to first destroy the entire US Pacific Fleet at Pearl Harbor. Then while the Americans were reeling, they aimed to seize the US military outposts at Guam, Wake Island, Midway, and the Philippines. The territory the Americans controlled was rich in raw materials needed to continue the war, such as rubber. The Japanese were mostly successful in executing their plan. The American fleet was severely defeated at Pearl Harbor, and all its pacific holdings were lost.
Japanese success began to run out at Midway, in June of 1942. Most of their fleet was destroyed in the battle, which lasted June 4–7. America's aircraft carriers (which escaped defeat at Pearl Harbor) and fleet struck a decisive blow. The Japanese could not replace the 4 aircraft carriers along with all the experienced pilots they lost. Around this time Americans also came up with new, successful tactics to beat the legendary Zero fighter planes. As a result of these changes, the offensive capabilities of their navy were effectively over for the rest of the war. The Doolittle Raid, which happened in April 1942, forced the Japanese to keep a sizable portion of their fighters at home instead of deploying them elsewhere.
By 1942 the American industrial power was in full swing and was able to outpace Japan in armaments production. The losses of their Pacific holdings did not stop America from finding raw material to power its war machine elsewhere. The British as well as her Australian allies were able to start diverting resources to Asia. A threat from the Soviets always loomed, so a contingent of Japanese forces had to remain on the Mongolian border, too. Japan was finally forced to defend all the gains it had made, and it was ultimately not able to do so.