With Nazis, the crux of the matter is this...even by American standards, conservatives must believe that there are certain qualities to human life which are transcendent and unchangeable whereas the Left believes that everything is ‘perfectible’ (changeable)...while the Nazis believed in strong centralized control (Left wing by American standards but Right wing by pre WW2 European standards) they also believed in certain unchangeable qualities (racial identity being primary among them) just different qualities from what the American conservatives believe...in this sense they were ‘Right wing’. Does that make sense?
The fundamental divide between Left and Right is their views of human nature. Leftists believe that human nature is a blank slate, that if you engineer the perfect society, you will also engineer away human nature. Maoism is probably the most extreme example of this, they even tried to socially engineer away differences between the sexes by forcing men and women to act, dress, and work identically.
The Right believes that certain aspects of human nature are innate and immutable, and that no amount of social engineering will change the fact that people, as individuals and as groups, are different and unequal. Nazism took this to the extreme of saying some ethnic and racial differences trumped all else. It's certainly a perversion of rightwing ideology, but nevertheless grounded in rightist thinking.
For Marxists, your social circumstances determined your identity. For fascists, your identity determined your social circumstances. This is why these ideologies were mortal, irreconcilable enemies. The fact that they both used a strong centralized government to implement their ideologies is peripheral - it's a means to an end, not the end.
Most people will acknowledge that anarchists are/were Leftists, so even in the US, the notion that "small government = conservatism / big government = liberalism" is nonsense.
There are both leftists (anarchists) and rightists (libertarians) who want minimal government, just as there are leftists (Communists, socialists) and rightists (fascists, monarchists, theocrats, military juntas in Latin America) who want strong central government.
The reason for this is that what matters isn't the size of government that you want, but what aims you want that government to achieve or not to achieve.
Being a Judaic Theocrat, I've figured a few things out over the years of struggling with these issues, ie, why Judaism is considered anathema by the traditional "right," why so many Jews are liberals, etc. Here is my understanding as of now:
In its ultimate form "right" advocates the supremacy of local custom over universal truth. The implication is that because they worship the G-d of Heaven instead of a local "gxd" rooted in the landscape that Jews are subversive and corrosive.
Taken to its ultimate form (at least the one it would have had before it went nationalist) the "left" advocates the plowing under of all local customs and beliefs in the name of a universal truth, but a "truth" that is reduced to the purely physical. From the traditional Judaism perspective both are wrong.
Jews are indeed "programmed" in a sense to destroy local "gxds"--because local "gxds" are false. They are supposed to spread the knowledge of the True G-d, the G-d of Heaven, who is infinite and ultimately outside the universe itself, unlike so many "gxds" worshiped by non-Jews. Jewish liberalism is indeed a perversion of this genuine Jewish mission, but HaShem nevertheless providentially uses it as He uses everything.
Of course "right" and "left" within the American context or simply as easy reference points are something else again, and quite valid.