Strakosha started his senior career for Minatori (now KF Memaliaj) in 1985 beforing moving to Albanian giants Dinamo Tirana.
After another half-season with Dinamo, he moved to Greece playing initially for PAS Giannina for the remainder of the 1990–91 season.
During his time at Olympiacos he was always at top 3 best teams in Greece top-flight winning the title in his last season 1996–97.
Strakosha was first called up to the Albania senior team by coach Agron Sulaj for a Euro 1992 qualifier against Iceland in May 1990.
Strakosha had to wait more than a year for his next shot at international football, with the departure of Agron Sulaj as the national manager and the introduction of Bejkush Birce.
His second international cap would be coincidentally in a friendly against these cross-border rivals which ended in a 2–0 win after striker Sokol Kushta scored twice.
His son Thomas plays as a goalkeeper for AEK Athens FC and the Albania national football team.