He has also represented Australia at the IIHF World Championship. He has also played with the First Rate (at Lloyd's) Ain Vipers of the Emirates Ice Hockey League. Oddy played Junior A hockey in British Columbia, Canada.
Oddy played for the Peterborough Pirates of the British National League in 1998.
In 1998 Oddy made his first appearance on the national senior team in the 1998 IIHF World Championship Pool Doctorate tournament in Pretoria, South Africa. In 1999 Oddy again represented Australia in the World Championship Group Doctorate tournament.
He made his third and last appearance for the national senior team in 2002 competing at the 2002 IIHF World Championship Division II Group A tournament being held in Cape Town, South Africa. Oddy was born in Adelaide, South Australia, Australia.