Interesting thread. I will admit to having skimmed parts of it, so maybe some of these points have already been made, but for what it is worth: (1) A Japanese War with the Soviets in 1937 probably means no Sino-Japanese war, as several people mentioned. That means that the Germans and Nationalist Chinese continue their economic quasi-alliance, with the Germans training and equipping Nationalist divisions in exchange for scarce raw materials, especially tungsten. That strengthens both the Nationalists and Germans to some extent in the years leading up to World War II.
(2) With Japan tied up in Manchuria, the Brits see much reduced pressure from the Japanese threat in the Far East and may feel that they can act more aggressively in Europe. The British nightmare was a simultaneous war with Germany, Italy and Japan with the US neutral. That threat hung over them in their response to European events like the one over the Sudetenland. We can't necessarily assume that British responses in Europe would be the same if the Japanese were off the board as a threat.
(3) The European and US response would depend on how well the Soviets did in the war. If they looked to be kicking Japanese butts in a strategic sense--as in looking as though they were about to take all of Manchuria, the US would essentially look the other way while US manufacturers poured "civilian" but dual-purpose goods into the Japanese islands, like trucks and radios. Before their atrocities in China, the US saw Japan as a useful counterbalance to the Soviet in the Far East, so they would tilt pro-Japanese, especially if the Japanese started losing.
(4) If the Japanese appeared to be losing in a major way in Manchuria, the Japanese had the ability to redirect their priorities from the navy to the army, though internal rivalries would make that difficult. You can make a lot of 15 to 20 ton tanks from the resources that went into one 70,000 ton battleship. Unless the Soviets were able to push the Japanese out of mainland Asia in a matter of weeks to a few months, the Japanese would gain in firepower and tank numbers as the war went on.
(5) The Soviets probably would not be able to pull off anything like a blitzkrieg over the Japanese in 1937, despite a relatively weak enemy. The Soviets, even as late as summer 1941 had a bad habit of producing lots of major weapons systems--tanks, airplanes, artillery, without producing enough of the stuff that made those systems effective, like spare parts, trained mechanics, ammunition for artillery, radios, enough tanker trucks to keep tank divisions supplied, etc. That's probably an inevitable feature of a command economy with a guy like Stalin at the top. The historic border skirmishes with the Japanese didn't last long enough or cover enough ground to uncover those problems, but an attempt at a bigger offensive would have. That's a two-edged sword. An attempt to take Manchuria in one swell foop in 1937 would be a fiasco, but the Soviets would be able to spot and eventually fix those issues in a more forgiving environment than fighting the Germans.
(6) If the Soviets pull out of Spain or offer only dribbles of aid to the Republicans, the Nationalists probably win by early 1938, which means that the Italians don't get as economically drained by the Spanish Civil War and are able to rearm somewhat more effectively in 1938 and 1939. That probably doesn't counterbalance increased British power in the Middle East because they don't have to worry about the Japanese as much.
(7) If the war goes on long, both the Soviet and Japanese will start running out of hard currency. That will hurt the Japanese more because they import more raw materials, but it will mean that the Soviets have less money to invest in machine tools they can't manufacture locally, which would cut back their manufacturing capacity in World War II, assuming the war comes.
(8) The Japanese army would in some ways be better in 1937 than it was in 1939 because it hadn't had the easy victories against warlord armies in China to make it overconfident and given to bad habits.