In their first party programme of 1920 the NSDAP did use some rhetoric apparently inspired by the sociaists, promising to "ban effortless income" (point 11.), confiscate all "profits made with war" (12.), introduce "gain sharing" with all the workers of "large firms" (14.), create of a "healthy" middle class and introduce an "instant ban" on the "large department stores" (16.) and in point 18. they promised to socialize all soil for "common use".
Naturally none of it was pulled through after they have actually gained power.
The NSDAP put out a 25 point plan in the 1920s. As stated below a number of these were socialist. However, as time went on quite a number of those in the NSDAP moved further to the right, especially those in the leadership such as Hitler. Hitler spent much of the 1920s being supported by rich industrialists, who gave him money, gave him a place to sleep, etc.
By the time 1933 rolled around the 25 point plan was basically forgotten and/or ignored. When those such as Roehm complained that the revolution should continue and to implement socialism Hitler implemented the Night of the Long Knives, which included the assassination of those in the party, such as Roehm, who belonged to the NSDAP's left wing faction. Hitler himself found economic matters to be boring (if not beyond his understanding) and his usual orders when making a decision brought before him was to make sure it wasn't socialist.
An example of someone in the party who had been quite socialist but ended up supporting the party's move to the right was Goebbels. He had to do quite a bit of soul searching to support the party, and Hitler, moving to the right.
Edit - spelling
The progression was DAP (1919) -> NSDAP (1920) -> NS (1933).
The DAP or Deutsches Arbeiterpartie seemed to have been started by Drexler and Harrer with a mixture of nationalist and socialist ideas (as well as anti-semitic ones). Not nearly as left as the Spartacists, but certainly for the workers and with a membership drawn largely from Drexler's place of work (Munich railway works).
/u/panzerkampfwagen mentions more about the NSDAP, but there was a rapid shift to the right, with a certain Mr Hitler steering the DAP in that direction from Sep 1919 onwards.
The Nazis wanted to appear pro-worker as best as possible. What better way than to claim your party is following an ideology that working people should democratically and directly control society ? It certainly had been working well for the KPD in gaining massive support. The KPD (German Communist Party) was hugely popular in post WW1 Germany and the Nazis began to capitalise on populist rhetoric to win over the German masses. After they cemented power in the early 1930s, they spent the first few months of their rule persecuting, imprisoning, and killing the entirety of the German left-wing opposition.
The Nazis gained support from the richest class of German society, who for the most part became party members, as well as from abroad in the West before the war started.
The Nazis used the word socialist in order to gain traction with the German working class and to draw support away from the communist party.