"Soviets were lefty, Nazis were right-wing."
Nazis were to the right of Stalin, but hardly right wing by our own standards. I recall reading a speech on The Propaganda Archive, of Goebbels going on and on about "We are Socialists!"
I found a similar archive a while back. Makes for some interesting, if disturbing, reading.
However they may have started, by the time they took power, the Nazis were a conglomeration of the most conservative political forces in Germany: The Militarists, the Nationalists, the Monarchists, and the Freikorps. I don't think that any of those had a left-leaning bone in their collective bodies. The left in Germany (communists, et. all) had mostly been driven to emigrate or driven underground by the end of the 20's.