Odman started his music studies in Sweden as an AFS exchange student in 1999, then received a full scholarship to Istanbul Bilgi University in 2001, where he obtained his B.A.

He spent two years playing in New York City while pursuing his graduate degree, performing and recording with Brian Lynch, Vincent Herring, Peter Washington, Benny Golson, Jacky Terrasson, Mike Moreno, Sean Jones, Ernie Watts, Stefano di Battista, Bertha Hope, Jim Rotondi, Alan Broadbent, Alex Sipiagin, and David Berkman.

Odman also played with a number of vocalists, including Sheila Jordan, Kevin Mahogany, Allan Harris, Mark Murphy, Deborah Davis, Ive Mendes, and Hilary Kole.

[3] In 2010, he released Nommo,[4] featuring trumpeter Brian Lynch, saxophonist Vincent Herring, pianist Burak Bedikyan and bassist Peter Washington.

In 2011, he released Autumn In New York, featuring trumpeter Terell Stafford, saxophonist Vincent Herring, pianist Anthony Wonsey and bassist Peter Washington.