The league of nations was basically a joke by 1936, after the Second Italian invasion of Ethiopia. Any change after that date that keeps it alive just means it keeps being a joke.
If, in 1920, the US voted to join, and the league had the power to do more than complain, possibly by making its presence felt on Japan after the invasion of Manchuria (1931), backed up by at least a threat of force, Hitler will probably be a bit more cautious (and may not even get in to power) - so it is quite likely ww2 as we know it doesn't occur.
- BNC