He competed in two Olympic Games and four gymnastics World Championships. His first Olympics was in 1928, where he took silver in the team competition. At the World Championships, he took three golds in the team competition.
In 1926, 1930 and 1938.
He also took a team silver in 1934. From 15–16 November 2008, an international gymnastics event was arranged in memory of Gajdoš.
January Gajdoš Memorial 2008 in Brno.
Switzerland won the competition. Individually, he won no medals, but he finished fourth in the horizontal bar, and eighth in the rings. At the next Olympics, in 1932, he again won no medals, but the team finished fourth in the team competition. Individually, he took two silver medals in 1926. In 1930, he took overall silver, behind Josip Primožič, and also won bronze in the pommel horse and rings. In 1934, he won no individual medals, but took sixth place overall. In his last World Championships, in 1938, he won gold overall. He also won gold on the floor.
