That date 1920, when they established the party, long before they had any power, they put the word socialist in there to appeal to the working class. The word had different connotations a hundred years ago in Germany than it does here today.
You can read the explanation here. The Nazis placed great emphasis on private property and free competition. They were against international capitalism, which they saw as Jewish.
Following the year you mentioned, in the 1920's a left wing group of nazis formed following the Strasser brothers. After Hitler solidified his power in the early 1930s, he wiped out the Strasser socialist views from his party.