He excelled in both the academic and athletic fields at St. Patrick's College, Thurles, before later studying at Maynooth University.
He was a regular member of the starting fifteen over the next few years and won a set of All-Ireland and Munster medals in his debut season.
O'Dwyer was also included on the Tipperary team that toured Belgium as part of a pan-Celtic initiative in 1910.
In 1920 he joined the Maynooth Mission to China, eventually rising to the position of Superior General in 1924.
At the time of his death on 13 February 1975, O'Dwyer was the last surviving member of the 1908 Tipperary All-Ireland-winning team.