Oddner was a jazz musician and studying advertising in the 1940s when he first came into contact with photography through John Melin, art director at Svenska Telegrambyrån in Malmö, the largest advertising agency in Scandinavia.
From there, Oddner began working a variety of advertising jobs, including industry, architecture, and clothing, as well as for SAS.
In the mid-1950s Oddner traveled to California, South America, the Soviet Union, and the far east.
With Sten Didrik Bellander (1921–2001), Harry Dittmar, Sven Gillsäter (1921–2001), Rune Hassner(1928–2003), Hans Malmberg and Lennart Olson (1925–2010), Hans Hammarskiöld (1925–2012), Tore Johnson, and Pål Nils Nilsson, he was a member of the professional collective Tio Fotografer ('Ten photographers') formed in 1958, and their subsequent photo agency Tiofoto.
His favorite photographers included Henri Cartier-Bresson and Richard Avedon.