Considering that the British fought the Opium Wars against China, and lots of European colonial powers effectively divided China up into 'zones' where they could trade, why were the Japanese able to then go on to conquer much of China? Why didn't they also have to defeat the Europeans, who presumably would've still seen their parts of China as in their interest? Or had the European influence in China already collapsed by the time Japan invaded?
Essentially, because they couldn't stop them. At this time period, the League of Nations was powerless as an entity. Although they had some successes with economic sanctions against smaller nations like Yugoslavia in their invasion of Albania, they were hamstrung against Italy who managed to get past the sanctions from the invasion of Abyssinia and his actions on the Greek islands, even trading with Britain and France (the main powers in the League) for their oil. This, combined with the very real threat of the Nazis who suddenly gained power and began to rearm the military, made any attempts to stop the Japanese merely impossible. The LoN simply didn't have the capability to both rearm at home, defend Europe and defeat the Japanese through anything but sanctions (which, like Italy, were simply barely enforced). The invasion of '37 did alarm the powers somewhat though, but nothing more than a backless warning was given, especially seeing as the Europeans were already weary of a war even against Germany. The influence the Europeans had was largely respected, though hot, until war finally broke out between them.