Strienz made his debut in 1922 at the Deutsche Oper Berlin as a hermit in Weber's Der Freischutz. In subsequent years, he performed at the opera houses of Wiesbaden, Kaiserslautern and Stuttgart. His roles included Mephisto in Gounod's Faust and Van Bett in Lortzing's Zar und Zimmermann, as well as numerous Wagnerian roles.

Between 1926 and 1933, Strienz worked for the newly founded Westdeutscher Rundfunk in Cologne. After the seizure of power in Germany by the Nazis in 1933, broadcasting director Ernst Hardt was dismissed, Strienz joined the Sturmabteilung and was engaged by the Berlin State Opera. In 1935, he recorded Deutsch sein,heist treu sein! and Flieg', Deutsche Fahne Flieg'! on the Electrola label, and subsequently became a popular performer on radio. In 1936 he sang in the Nationalsozialistische Kulturgemeinde produced film Ewiger Wald. He continued to take operatic engagements and guested at the Royal Opera House, Covent Garden. In 1937 and 1938, he sang Sarastro in a recording of Mozart's opera The Magic Flute with the Berlin Philharmonic under Sir Thomas Beecham. He was also known for his interpretations of the ballads Der Nock by August Kopisch and Die Uhr by Johann Gabriel Seidl, set to music by Carl Loewe.

Because of his great popularity, the Nazi regime called on him after the start of World War II to perform on the popular radio music show Wunschkonzert fur die Wehrmacht, where he was known, among other things, for performing Gute Nacht, Mutter by Werner Bochmann. From 1940 he recorded various war songs as a soloist. He also appeared in the propaganda films Wunschkonzert (1940) and Fronttheater (1942). In the final phase of the Second World War, Adolf Hitler included Strienz in the Gottbegnadeten list as one of nine major concert singers in August 1944, exempting him from military service during the final stages of the war.

In the immediate post-war period, German broadcasters, especially in the Soviet occupation zone, boycotted him as his name was associated with the Nazi propaganda of the war years. Strienz continued his singing career, making successful tours and receiving a record contract from Decca. Strienz ended his singing career in 1963 and retired into private life.