Oenone achieved success as a road cyclist in Australia, including the Bay Criterium Series, and the Geelong Tour.
She had great success overseas, particularly winning stages of the Giro d'Italia Femminile (ITA) and the Points Classification for the Giro d'Italia Femminile in 2004 and 2005, as well winning the UCI Women's Road World Cup series in 2004 and 2005. In the 2004 Summer Olympics Women's Road race she was in the leading group with fellow Australian Sara Carrigan, and when Carrigan and Judith Arndt broke away in the final lap to win the gold and silver medals, Wood had to sprint for the bronze medal with Olga Slyusareva of Russia and Nicole Cooke of Great Britain, coming 4th overall in the race.
She won the Women's Time Trial at the 2006 Commonwealth Games in Melbourne, also winning the silver medal in the Women's Road Race, behind fellow Australian Natalie Bates.
She was the 2004 and 2008 Australian Open Road champion (in the Elite Women's Road Race event).