Strokosch has represented Scotland in various competitions with the 'Sevens' and 'A' teams, his first full international cap for the Senior Scotland squad being on 25 November 2006 against Australia.
Strokosch is a member of the Scottish Institute of Sport. At the age of 12 became a black belt in karate, later representing Scotland at the European and world Under-21 karate championships. His father is German and his mother Scottish.
He was selected in the Scotland squad for the 2015 Rugby World Cup. He announced his retirement from international rugby on the 5th November 2015.