At the beginning of the German invasion of the Soviet Union in June,1941, Strauch assumed command of a unit of the Einsatzgruppen.

Strauch led Einsatzkommando 2, part of Einsatzgruppe A, which from 4 November 1941 was under the command of Franz Walter Stahlecker.

On 30 November 1941, he participated, with 20 men under his command, in the murder of 10,600 Jews of Riga in the Rumbula forest near the city.

In July 1943, the Nazi general commissioner for White Russia reported on having had a conference with the "extremely capable [...] chief of the SD, SS-Obersturmbannführer Dr. jur.

Despite an effort to sham mental illness, Strauch was convicted by the Nuremberg Military Tribunal in the Einsatzgruppen Trial for having a key role in the Rumbula and a number of other mass murders in Eastern Europe.