O'Dwyer was born in Kilkenny to his sporting parents Paddy O'Dwyer, a judoka who competed for Ireland at the 1975 World Judo Championships in Vienna, Austria, and Gudrun Marx, an East German-born eventing rider. O'Dwyer attended both primary and secondary school at CBS Kilkenny, where he began his athletics career and lettered in the sprint races and long jump. At the age of 13, O'Dwyer grew exceptionally taller and turned his attention to high jump. Since then, O'Dwyer excelled the sport, and had an initial jump of 1.86 m, until he extended it tremendously to 2.01 to establish a high school and junior record in 1999.