A full international between 1982 and 1990, he won 52 caps and scored 7 goals for the Sweden national team, and represented his country at the 1990 FIFA World Cup.

Strömberg was a part of IFK Göteborg's youth teams before making his senior debut for "Änglarna" on 16 April 1979 in an Allsvenskan game against Kalmar FF that ended 4–0.

He made his senior international debut for Sweden on 3 June 1982 in a friendly 1-1 draw with the Soviet Union, playing for 68 minutes before being replaced by Karl Gunnar Björklund.

Since he has no managerial experience, he was never regarded as a serious candidate to succeed Lars Lagerbäck as head coach of the Sweden men's national football team.

In interviews during the 2006 FIFA World Cup he said that he was flattered to get mentioned as a potential candidate for the job and that he would think carefully about any offer from the Swedish Football Association.