He debuted for Vorwärts Steyr, and later played for First Vienna Football Club. While with First Vienna, he went on a tour of the Middle East and upon returning was arrested along with two other players for smuggling narcotics into Austria. Strittich was imprisoned for three months and banned from football for one year by the Austrian Football Association. Unable to play football in Austria, Strittich was recruited by Béla Guttmann to play for Italian club University of Southern California Triestina.
The Austrian FA would not clear him to play, so he joined Colombian side Bananeros Santa Marta, where he could play because the Colombian Football Federation was not at the time affiliated to Fédération internationale de football association. Upon returning to Austria, Strittich learned that his ban was still in effect, as the Austrian FA ruled that he did serve the ban while playing in Colombia.
He moved to Switzerland and trained with the youth side of Young Fellows Zürich. Next, he briefly returned to Vienna, and was sold to French side Besançon Remote Control after just six months.
He suffered a back injury in France, and would retire from playing soon after. He made his debut for Austria in December 1946 against Hungary and earned 4 caps, scoring one goal.
After retiring as a football player Strittich worked as a coach for Sturm Graz in his home country.
However, his greatest success as a coach came in Denmark, where he made Esbjerg fB champions in 1961, 1962, 1965, and 1979. He was also coach of the Denmark national football team from 1970 to 1975. As a player As a manager.