Having appeared 9 times for the Sweden U21 team, Strömberg made his senior international debut for Sweden on 3 June 1982 in a friendly game against the Soviet Union. He scored his first international goal on 29 May 1983 in a UEFA Euro 1984 qualifying game against Italy which Sweden won 2–0. A few months later, Strömberg scored two goals as Sweden beat Italy 3–0 away in the same qualifying campaign. Despite the two victories against Italy, Sweden failed to qualify for Euro 1984.