Well first and foremost, the "Axis" that you referred to is not a monolithic entity, but rather, an alliance of world powers with their own vested interests, their own reasons for war, and their own justifications for military expansionism. So judging from how your question is framed, by "Axis" you seem to be referring specifically to Germany, but I will attempt to unpack your answer in as nuanced and comprehensive way as possible.

Many in the Japanese military saw the expansion of their empire as a means of becoming a modern state in the eyes of the world, on par with great European powers at the time. Furthermore, Japanese framed the rhetoric of this expansion within a dialogue of "Pan-Asianism", and the protection of Asian interests from white imperial powers in the West (namely Britain and the United States). Many Asian countries, be it the Philippines, China, Thailand, etc. had a long history of both military and economic subjugation at the hands of European and American imperialism. In this regard, the Japanese fighting allied troops in the pacific did not see themselves as agents of genocide, but rather, as protectors of a sort of paternalistic guidance of Asian independence and progression, with conveniently, Japan as the father figure protecting their fellow Asian "wards" within that paternalistic setting.

In regards to Germany, I think it is instructive for us to use an approach similar to Mary Renda's in her account of the U.S occupation of Haiti by asking the question: How does one imagine themselves when they pull the trigger of a gun? Again, engaging directly to your question, is it likely that the common German soldier saw himself as a vessel of genocide? Or, is it more likely that the background of the soldier in a prewar context (their class, their regional identity, their experiences with Jews before the war, the relationship to economic depression and recovery, etc.) shaped their attitudes and motivations going into the war? Some surely did see themselves as actors in the genetic purification of the German race, however, I would postulate that these were the minority of soldiers. Some saw themselves as restoring the glory of the German empire. However, as [Stephen Fritz] (http://www.amazon.com/Frontsoldaten-German-Soldier-World-War/dp/0813109434/ref=sr_1_4?s=books&ie=UTF8&qid=1413870497&sr=1-4&keywords=german+soldiers+of+world+war+two) suggests, many others saw themselves upholding the less sinister values of National Socialism against the forces of communism and capitalism. National Socialism was more than just the idea of ethnic purity. We have to remember the context of post WWI German society; its political unrest of the Weimar Republic and its economic hardships. The soldiers of Germany experienced this context, it memory was palpable and vivid, and thus, many saw the country's renewed glory as intrinsically connected to the class, economic and political ideologies of National Socialism.

I do not have a comprehensive background in Italian history or Italian fascism, so I won't attempt to postulate on the motivations of soldiers in that context. However, I would just like to end by cautioning you of the approach that leads to questions like this. What you are doing is taking a presentist mindset, the knowledge and context of the present and imposing it on your inquiry of the past. In so doing, you devoid the subjects of your presentist thinking of their historical contexts, and in turn, pass judgment onto these historical actors and ascribe motivations that were either nominal or secondary to their lives and beliefs. This is not an attack on you, or, an attempt to scold you in an academic sense. Rather, it is simply an attempt to illuminate some the fallacies that everyone (including professional historians) bring with them that shape their historical scholarship. In the future, try to refine your inquires by identifying possibly presentist ideas and analysis. Again, I don't want this to seem like an attack, I am glad you are attempting to think about the motivations of the other in a historical context.

I hope this answer shed some light on your question and the historical contexts the shaped the more forgotten actors of the Second World War.

Further Reading:

[Japan at War] (http://www.amazon.com/Japan-War-An-Oral-History/dp/1565840399/ref=pd_sim_b_1?ie=UTF8&refRID=1XVS7YD9VBYY91RB6N5B)

[The Programme of NSDAP] (http://www.amazon.com/Programme-Nsdap-Gottfried-Feder/dp/1908476885/ref=sr_1_11?s=books&ie=UTF8&qid=1413871347&sr=1-11&keywords=national+socialism)

[Japan's Total Empire] (http://www.amazon.com/Japans-Total-Empire-Manchuria-Imperialism/dp/0520219341/ref=sr_1_8?s=books&ie=UTF8&qid=1413871476&sr=1-8&keywords=japanese+imperialism)

EDIT: Spelling and formatting and junk.

I was just re-reading The Second World War by John Keegan, specifically the chapters on the campaigns in Africa and Italy. He suggests that general Italian attitudes towards the Allies were a mild Francophobia and a strong affection for the US (influenced by emigration), and that this influenced their resistance (or lack of) when things went bad for them. (He mentioned some "defenders" in Sicily who helped unload the boats of the attackers.)

It should also be noted that Mussolini's Italy was racist, as in the brutal race laws (excerpt from Jews in Italy under Fascist and Nazi rule, 1922-1945) and colonizing Africa, but not genocidal.

Also, can we say that "the Axis" was a thing? Though it was convenient for both sides to propagandize that it was. As I understand it, Mussolini was first opposed to Nazi Germany and supported Austria until the Anschluss broke his strategy; even after, Mussolini tried to be independent and appear as an equal partner (however badly chosen his targets were, however tiny the economy was in relation to Germany, and however inferior the equipment). Germany declared war on the US, apparently to induce Japan to declare war on the Soviet Union, but Japan cheerfully avoided doing that, so they didn't really cooperate.