Josef Strasser, Peter's father, was a leading functionary of the Social Democratic movement in Reichenberg, Bohemia, before World War I, then part of Austria-Hungary.
After the Nazi occupation of France, he lived underground and collaborated with the Resistance, but was arrested and handed over to the Gestapo.
After a brief stay in a concentration camp, the regime forced Strasser to work as a welder in a German armaments factory.
The next day, supporters of the SPÖ under Strasser's chairmanship in the Vienna City Hall decided to found a socialist youth organization; the proposal by the Communists to do this jointly with them was not followed.
After Strasser's death, a large cooperative building at the end of Landstraßer Hauptstraße in the 3rd Vienna district was named Peter-Strasser-Hof.