A product of America's most prolific hockey hot bed, Eveleth, Minnesota, Almquist played goal for the high school team from 1923 through 1927. After a two-year interval with Virginia of the Arrowhead Amateur League, he entered St. Mary's College at Winona, Minnesota. At St. Mary's, he played four varsity years and was named both team captain and to the All American team in 1932-33. Almquist returned to Northeastern Minnesota after graduation to begin a four-year professional career, first with hometown Eveleth in the Central League, followed by three seasons with St. Paul in the American Hockey Association. During this period, he was named to league all star teams in both the 1933-34 and 1935-36 seasons.
The coaching career for which he would become legendary, began at Williams, Minnesota in 1937. That year, he coached the high school team to a second-place finish in the district. The following year saw Almquist move to Roseau where he coached the high school "B" team until 1941, while at the same time playing for the amateur Cloverleafs. He also coached the amateurs for one season and continued to play for them through 1943. In 1941, the Eveleth native became Roseau's head coach, a position he would hold until 1967. During this period, Roseau High School became a perennial power winning state titles in 1946, 1958, 1959, and 1961. Roseau appeared in the state event fourteen times, and in addition to the state championships they were runner-ups on four occasions, third place finishers once, and captured two consolation titles. When Almquist gave up coaching to become strictly athletic director and high school principal, his teams had posted a record of 404 wins, 148 losses, and 21 ties. During the 1957 through 1959 seasons, the Rams ran off a string of 49 victories without a loss.
In recognition of his career achievements, Oscar Almquist was made an honorary life member of the American Hockey Coaches Association in 1969 and was elected to the Minnesota Hockey Coaches Hall of Fame in 1982. In the words of Bernie Burggraf of the Roseau Times-Union, as far as hockey is concerned, he is truly a "Giant of the North."