Maja Odžaklievska began her musical career as a 15-year-old girl, appearing at an audition for Radio Skopje. In 1970, she moved to Belgrade. Radoslav Grajić invited her to participate in the radio show "Maksimetar", which she won and then received a supporting role in an adaptation of "Rabelais" by Jean-Louis Barrault. She has participated in numerous festivals throughout the former Federation including several candidatures at the Eurovision Song Contest.
In 1982, Odžaklievska competed in with the song "Julija", scoring 57 points and placing second. She returned to the competition the following year in 1983 with the song "Lidu Lidu Du" and scored 46 points and placed third. In 1984, she entered once again with the song "Niki", scoring 51 points and placing second. Her final participation was in 1988, performing "Te Ljubam Ludo" with group Gu-Gu. They scored 42 points and placed sixth.
In 2006, Odžaklievska took part in the selection to represent Macedonia in the Eurovision Song Contest 2006 with the song "Koj pat da izberam". She finished ninth in a field of 20 songs.
On 2 March 2013, Maja competed in Beosong 2013, the national final to select the Eurovision entry for Serbia with the song "Anđeo s neba". Her song did not advance from the semifinal.