Odqvist was born on 9 January 1913 in Uppsala, Sweden, the son of lieutenant colonel Hjalmar Odqvist and his wife Ella. He grew up in Strängnäs where his father was an officer in the Södermanland Regiment. He passed studentexamen in 1932 and trained as an officer at the Military Academy Karlberg. Odqvist became an officer in 1935 when he was commissioned as fänrik in the Södermanland Regiment. The Swedish Air Force was now under strong construction, which attracted him. He joined the Air Force, underwent pilot training at the Swedish Air Force Flying School, finishing in 1937. He became lieutenant in the Air Force in 1939 and captain in 1942. Odqvist completed the staff course of the Royal Swedish Air Force Staff College from 1944 to 1945 and then served in the Air Staff. He was teacher at the Royal Swedish Air ForceStaff College and the Artillery and Engineering College from 1944 to 1949 when he was promoted to major. Odqvist then served as chief of staff in the First Air Group from 1949 to 1951 and then as commanding officer of the Swedish Air Force Squadron Leader School from 1951 to 1952 when he was promoted to lieutenant colonel. Odqvist was commanding officer of the Flygvapnets krigsskola from 1952 to 1954 and the Västmanland Air Force Wing from 1954 to 1959. In 1955, Oqvist was promoted to colonel and from 1959 to 1961 he was Vice Chief of the Air Staff. He was appointed commanding officer of the Fourth Air Group in 1961 and the year after he was promoted to major general. In 1964, Odqvist was appointed Chief of the Air Staff and in 1966 he was appointed commanding officer of the First Air Group. He left the position in 1973 and retired from active service and was then also promoted to lieutenant general. After retirement, Västerås became his home town. He was unanimously elected to chairman of the F 1 Kamratförening, a position he held until 1990, when he became honorary chairman of the association. Odqvist was chairman of the Swedish Aviation Historical Society from 1974 to 1978 and governor of the Rotary International's district 234 from 1979 to 1980. He became honorary member of the Swedish Aviation Historical Society in 1982.
Personal life
In 1938, Odqvist married Märta Sundell, the daughter of the Ernst Sundell and Elin. He was the father of Eva, Kerstin, Ulla and Inger. His daughter Ulla, a diplomat, was one of the hostages of the 1975 AIA building hostage crisis in Kuala Lumpur. The farm Kalfsund in Överenhörna socken was acquired by the Odqvist's in 1941. His wife Märta died on 13 August 2003 and he on 15 February 2005 in Västerås. They are buried at Överenhörna Church, a few kilometers from Kalfsund.