An avid runner since early age, Odložil began training with a coach at a military school in Bratislava. At his first major competition, the 1962 European Athletics Championships in Belgrade, Odložil was eliminated in the 800 metres semi-final. Two years later he ran 1500 metres at the 1964 Summer Olympics in Tokyo. Peter Snell easily won the final, but Odložil managed to get silver ahead of John Davies. In 1965 Odložil set a new world record on 2000 m (5:01,2). The 1966 European Athletics Championships were disastrous for Odložil as he was eliminated already in the heats. He did better at the 1967 European Athletics Indoor Championships in Prague, taking silver in the 1500 m, but at the 1968 Olympics finished only eighth in the 1500 m. Odložil retired in 1969.