Most important: 1.Italy:Germany's only european ally with any industrial/demographical base 2.Romania:relatively large armed forces, main oil supplier 3.Hungary or Finland:Finland had the most effective armed forces of Germany's allies, but they were not very numerous, and did not really consider themselves as allies(Didn't they just refuse to advance any further in Russia after they had recovered the territories lost during the Winter War). Hungary was the last remaining of Germany's allies, after all the others had had joined the other side.
In terms of armed forces I'd say Finland was the toughest, most effective German ally. But Finland indeed was in it only to get back from Russia what they had lost in earlier wars; they picked the side of the one that would provide them with this. In terms of resources and strategical value, Romania had oil, period. Most of the other Axis allies had little value in combat and had the Germans end up either fighting them, or fighting for them... The Germans themselves appear to have valued Vichy-France quite a bit, relying on them to hold the western North African coast.
Hungarian/Romainian troops did fill out large stretches of the Eastern Front that Germany could not plug on her own... However, that Romanian oil was the best! Italy was probably the worst, by the time of WW2. Musso simply ran about the Med creating messes that Adolf had to go clean up, always distracting him from the prime task of conquering the Soviet Union.
The supplied huge numbers of men, but their worth in combat was shown at Stalingrad and other offensives; they were unable to protect the German flanks. Only Finnish troops were really capable of carrying out a task given to them independently.
Unless you're relying on them, and have a leader in charge who sees only numbers and not relative value of those numbers!
Well, Finland had the most effective army of the German allies. It just was too small to be really important for the Axis. Romania and it's oil was propably the most important. Italy was the worst. Germany lost much of forces when helping Italians. And after Italy surrended, Italy took lots of important forces from Germany. Maybe, without Italy, Germany would have win...
The trouble is, Germany needed Italy back in the 1930s, when Italy was the dominant power... Without Italy, for example, Germany would never have gained the Anschluss. Hitler had tried it earlier, but Mussolini moved troops up to the Brenner Pass in threat, and that stopped Hitler.
The germans were always fast at blaming Italy for their defeats, but in reality Italy was not the burden many think. Undoubtely, of all Germany's allies, Italy caused the biggest casualties to the allies. Also, Italy's invasion of Greece did not delay Barbarossa that much. What was more important was the military coup in Yugoslavia in march 41, in which the pro german yugoslav governement was replaced by a pro allied one. So Hitler decided that Yugoslavia should be occupied alongside Greece, which made the balkan campaign last for at least 3 weeks longer. Had it only been about helping the italians in Greece, Barbarossa would not have been delayed. Then, altough Germany had to send troops and planes to support Italy in the mediteranean, far more british and commonwealth troops were needed to face them, which again could not be used by the british elsewhere.(For example for threatening german positions in France or Norway....). So that's all relative. Italian troops played also a big and often forgotten role in figthing partisans in Yugoslavia. Also the italian fleet, tough ineffective, always forced the british to place an important part of their fleet in the Mediteranean, which could hace been used against the germans or the japanese otherwise. All in all if you consider how much forces the allies used against Italy, there is absolutely no comparison between Italy and Germany's other allies.
The most important and useful "could" have been Japan. With its mighty navy, a formidable airforce (initially) and a tough army. We all know what happened, Japan dragged US into the war and that was all she wrote.
Japan being an ally of Germany is debatable, I'd say. They were friendly to each other and hostile to the same countries, but to say they helped each other... The only true act of help would be Hitler's utter lunacy to declare war on the US.
Without Germany, Italy would have fallen in 1941. Italy caused losses to Allies, but you can't compare those losses for how much the Japanese caused. Italy alone had almost no victories in WW2, they lost everywhere until the Germans helped them out, which took much forces from Germany. If Italy would have wanted to be effective ally, it would had to wait until 1942. But no, Italy was greed and went for war too early. And got beaten badly. In Balkan, they were little more useful, chasing partisans for example, as you said. Italy's navy was pretty strong, but it wasn't used correctly. I don't know any reason for Germany to be Italy's ally in war. Of course, in peace time Italy was good ally, because of it's LARGE army. GB and France didn't know how poor it was.
Of course Japan was a much more powerfull ally than Italy, but the question was about Germany's european allies, and there it seems clear to me, that despite's it's many flaws, Italy was still the most important.
Italy was the biggest of Germany's allies in Europe. But for the German war efforts Italy was just a block. Without Romania's oil, Germany's tanks would have been almost useless. Italy was a important ally, but just a block for Germany's war efforts. (Try to understand what I mean).
I would consider them at least informal allies if the prime minister needs to step down in order to make a peace settlement with the common enemy at least remotely acceptable.