Oddbjørn Hagen started his skiing career as a ski jumper, winning the boys district championships for Hedmark at the age of 15. In 1931 he settled in Oslo with ambitions to climb to the national top in cross-country skiing and Nordic combined, and at Holmenkollen in March 1932 he had his breakthrough by winning the Nordic combined, beating the newly crowned Olympic Champion Johan Grøttumsbråten.
He won the World Championships and Holmenkollen in Nordic combined in 1934 and 1935, in addition to earning a silver medal in the World Championships in 1935 both in 18 km cross-country and Nordic combined. After returning home with one gold and two silver medals from the 1936 Olympics, he won the 18 km at Holmenkollen in his last big competitive appearance, but had to settle for second place in Nordic combined behind his Olympic teammate Olaf Hoffsbakken. Hagen trained very hard, and was always well prepared for important events. His strength was cross-country skiing, and he was an excellent relay skier who could ski both the opening and final leg with success. In ski jumping he was steady, but not outstanding. He worked in Oslo as a workshop manager until his retirement.