FDR was many things, but he wasn't a totalitarian thug who ordered the execution of prisoners. If he was, the US likely would have been no better than its enemies. And the US did happen to commit atrocities during the Second World War as a matter of policy, just not against POW's or occupied territory.
Now, let's be clear on what you're asking for. Any order to plunder, torture, murder, or rape either prisoners of war or the people of an occupied nation issued by any military branch of Japan, Germany, or the USSR.
"Military" does narrow it down a little bit--for instance, the only part of the SS that was really "military" was the Waffen-SS, which was separate from the SS departments that ran the concentration camps or rounded up the Jews. So I'm going to take the liberty of counting any state organization, including the SS and NKVD, not just the military itself.
Germany: If you're going to deny the Holocaust you're a very silly person and I'm not going to answer you.
Japan: Let's just start with Unit 731. http://en.wikipedia.org/wiki/Unit_731 That's not the end of it, and it's barely the beginning, but all you asked for was an existence proof.
Russia: The Katyn Massacre (http://en.wikipedia.org/wiki/Katyn_massacre), was carried out based upon orders signed by Stalin himself to murder Polish POW's and residents of Soviet-occupied Poland. Again, not comprehensive, but all you asked for was an existence proof. And I guess it might not technically count because NKVD are separate from military. Oh well.