No, there was never really any military cooperation between the two states during the war. The cooperation between the two states was limited to economic and scientific collaboration. Military collaboration was never really an option because Germany and Japan had different goals and neither side really possessed the capability to fight a war in a completely different part of the world. The Germans operated a few surface raiders in the Indian Ocean, but never really went beyond that. There was also a famous case of Korean Soldier (Yang Kyoungjon) conscripted into the Japanese Army being captured by the Soviets, than ended up being liberated by the Germans and fighting for them. But that was a rare case that wasn't really repeated.

There were numerous instances where they aided each other though. One of the more famous being the Automedon incident. A British ship named the Automedon was shelled and captured by a German surface raider. The ship contained important documents on it about British troop movements in the Far East, they were immediately given to the Japanese, and the documents helped convince the Japanese that the colonial possessions of Britain were weak and undefended, which helped pushed them towards war.

In terms of economic cooperation, Germany sent a number of engineers and industrialists to Japan in the years leading up to war. Japanese ship builders began to copy German designs in key areas, especially with regards to submarines. The Germans also sent key individuals associated with aircraft to inspect the Japanese air force. There was also limited collaboration between German aircraft companies and Japanese ones.

There was also limited forms of espionage cooperation. Wilhelm Canaris, the head of the German espionage agency, visited Japan to enlist the Japanese in forming an anti-Soviet spy ring. The German and Japanese intelligence services promised to share important details with each other and to cooperate. Supposedly they even came up with a plan to assassinate Stalin, but that didn't really get far. Again, once the war started the cooperation sort of died off as the two states become occupied with their own goals and ambitions.

Finally in the Scientific sphere,there was limited collaboration. Germany's radical social Darwinist found its way into the hands of Japanese radicals, who molded it too fit into East Asian society. There was also collaboration in the fields of biological and chemical warfare and several agreements were signed between Germany and Japan that made scientific collaboration easier.

Funny enough, there was more military cooperation, in the early years,between Germany and China. Germany sent officers to train the Chinese army, and some of these officers even helped the Chinese fight against the Japanese. There was also a large amount of Chinese officers who studied with the Wehrmacht, including the son of Chiang Kai Shek.

Source:

German-Japanese relations 1895-1945 by Christian Sprang

I have yet to run across any evidence of any sort of German and Japanese soldiers fighting together on any sort of a unit level. The closest thing that I can think off of the top of my head are some instances of Asian conscripts that were captured and re-conscripted a couple of times. This was very infrequent though. A prime example of this would be Yang Kyoungjong, a Korean who was pressed into service in service in the Imperial Japanese Army and sent off to fight against the Soviets in one of the early border conflicts between the two. The Soviets ended up sending him (among other prisoners of war) off to fight against the Germans on the Eastern Front. The Germans captured him, and then pressed him into service in one of their Ostbattalions (made up of former Soviet soldiers and defectors), where he ultimately ended up on the coastal defenses in Normandy.

So technically, yes. You've got at least one documented instance of a [former] IJA solider fighting alongside German soldiers on the battlefield. There are probably other instances here and there of soldiers that had similarly odd/bad luck, but AFAIK no SS units stationed on Iwo Jima.

Not Nazis, but interestingly enough the Japanese did participate in the Battle of Madagascar.

In Britain's first amphibious assault of the war, they attacked the Vichy garrison to secure the island, and prevent Japanese submarines from using it as a port. Three weeks after the initial invasion of the island, three Japanese submarines showed up and caused trouble, though the island fell after a few months anyway.

Nothing too epic, but an interesting show of solidarity between two unusual allies.

Hello there, friendly neighbourhood mod here.

I just wanted to post this comment that there is no need to continuously recommend the movie 2011 'My Way'. Whether or not it is historically accurate is a separate question and whether is a good movie to watch (it was almost unanimously critically planned, mind you) is also something for another subreddit. Unless it is a thread specifically asking for movie recommendations, we ask that you refrain from recommending movies on historical topics unless asked to. You are however more than welcome to recommend primary and secondary sources to supplement the answers already given.

Please keep this in mind before you post yet another comment recommending this movie.