The question as to whether or not the National Socialists are "socialists" is almost entirely meaningless at this point since the commonly accepted definitions of socialism are so vapid and divorced from historical context.
Nonetheless, Marxists are going to have to offer clear and principled explanations to these questions if they are to become relevant to the global Left once more.
So, are Nazis "socialists"?
At the time Marx and Engels wrote the Communist Manifesto they were very explicit in explaining that they were using to word "Communist" so that they could differentiate themselves from various "socialists" such as the Utopians and various 'reformers'. This touches on the core problem with defining socialism properly: it has never been a term for a movement with any set goal, but rather is a term that covers a broad spectrum of reaction against the negative aspects of Capitalist society.
In this sense the Nazis have some claim to being socialists, at least ideologically. They are socialists, however, in a way that is completely at odds with Marxist socialism, just as the Utopian cults in the United States had nothing to do with Marxism.
Marxism, in the sense of "what Marx actually wrote, rather than all that state-bureaucratic bullshit that dominated the Cold War", is about worker's control of society politically, economically, and for the most part socially, in a very "bottom up" way. It is about economic planning based around cooperatively meeting human needs and wants, and ending capital exploitation.
National Socialism was about purging Germany of "parasitic" peoples and concentrating power in the hands of a ruling minority who would restore the German people to greatness. In this way it was similar in many important aspects to Stalinist, "Socialism in One Country." The important difference is that Stalin (while being a grotesque monster who made a mockery of Marxism) at least paid lip service to ending exploitation of the working classes, and largely abolished the capitalist markets within the USSR (to disastrous effect, in many places they would have been better off under pure capitalism than under Stalin). In comparison the Nazis's central leaders never talked about ending capitalism, only ridding it of its "Jewish" and "anti-German" components.
So the Nazis, in rhetoric, were kinda socialists. In practice they really weren't (most of their nominally "socialist" reforms such as "abolition of the standing military and its replacement with the armed German People" they never even tried to implement) and even in rhetoric their claim to being socialists is tenuous at best.
The fundamental issue for Marxists is that the Nazis rejected entirely the core parts of our version of socialism: the self-emancipation of the working class, the abolition of all exploiting classes, an end to all forms of exploitation and repression (that of women, national/ethnic minorities, LGBT, etc), and international solidarity.
