Born in Memaliaj, Albania, Strakosha was Albania's national team goalkeeper from 1990 to 2004. He made his debut on 30 May 1990 and retired on 13 October 2004.
Strakosha played first for Minatori (now KF Memaliaj) and then Albanian majors Dinamo before Greek clubs Giannina, both Ethnikos -Piraeus & Asteras-, Olympiacos, Panionios, Ionikos, and Kallithea.
After his retirement, he became a goalkeeping coach. Until 2007 he was the Olympiakos goalkeeping coach, when he signed for the Cypriot champions APOEL FC.
Strakosha was first called up in the Albanian national team by coach Agron Sulaj for a Euro 1992 qualifier against Iceland in May 1990.
On the day of his first international game, he was already 25 years and 62 days old. The reason for such a late debut on the international stage was a surplus of qualified keepers in the Albanian international squads like the veteran Perlat Musta and the very promising youngster Blendi Nallbani
Due to Albania's staunch communist rule, despite his talent, Strakosha was playing in his country's domestic league as every single player in the international squad .
In his debut, Albania lost the game in Reykjavík 2–0 which added to their miserable run of 19 games without a single win. The game itself was not to be a special one for the rookie goalkeeper as he conceded 2 goals, which kept him aside for the following games.
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.
This game was played after the fall of Communism in Albania which meant that from there on, players would be allowed to play abroad for the first time in 45 years. A notable impact like this, struck directly to the national team since nine players – notably Sulejman Demollari and Edmond Abazi – would be playing in foreign leagues, the majority choosing neighbour Greece, the same way Strakosha did.
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.
Strakosha's career would follow up to the point to become Albania's most capped player, and achieving an extense career under the Eagle's goalposts.
Although living in Greece and being of Greek descent Strakosha chose to remain loyal to Albanian national team, a decision that was treated with suspicion in Albania and with a negative feedback in Greece. His mediatic exposition reached up levels up to being aired in the Greek TV on behalf of mis-treatment to Albanian immigrants in Greece, as well as hoping for friendship and understanding between the two neighbour countries.
In 2011, he became the coach of Albania national under-19 football team. He left Albania U19 on 12 August 2014 to work for Olympiakos, where he was succeeded by Altin Lala as Albania U19 coach.Kategoria superiore: 1989–90
Kupa e shqipërisë (2): 1988–89, 1989–90
Superkupa e shqipërisë: 1990
Greece Super League: 1996–97
Greek Cup: 1997–98