Did Organised crime, like the Italian Mafia, Chinese Triads or Japanese Yakuza play any role in any part of the conflict? either supporting their nation or in resistance?
The mafia certainly did play a role, as the Fascists had suppressed their activities but the western allies accepted mafia help during the invasion of Sicily and then on the mainland. This revived the fortunes of the crime gangs and they became a much bigger problem for the Italian government after the war.
In the US the American government and military made deals with the mafia on both US coasts to keep the ports open and prevent labour strife throughout the war it had a code name but I can’t remember it atm.
In the European theatre of war depending on which side was more advantageous for them organized crime played on both sides of the fence. Due to the huge amounts of supplies and materials the allies had there was a huge black market for those supplies and materials and organized crime was opportunistic due to the huge volume of traffic most of what was sold or bought on the black market was not generally missed.
On the axis side of things organized crime was generally muted until later in the war as the Nazis clamped down on organized crime hard and after the invasion of France organized crime took off as there was not enough police around to police them so as the war got worse for the Germans the organized crime gangs things got considerably better and even helped the allies with intel for a price of course.
In the USSR not much is really known due to the secretive nature of the regime of organized crime but it is thought that any crime that happened was sanctioned by the government.
In Japan the Yakuza supported the Japanese effort as like everyone else Emperor Hirohito was a god and was unquestionably followed and anyone who dared go against the emperor usually didn’t live long.