Odlum, who owned and edited a socialist newspaper called The Crusader for many years until his death, was one of the most vocal socialist politicians in Saint Lucia and in the Caribbean. He was a friend of Maurice Bishop, Fidel Castro and Muammar al-Gaddafi. He often criticized leaders of his own party such as Allan Louisy and Kenny Anthony for not supporting the masses enough. He was fired from his position as foreign minister both times for such comments. Odlum fought for higher wages for agricultural workers, particularly during the 1970s. Among his achievements was the establishment of relations between Saint Lucia and China. He was also one of "four musketeers" of the region. The name given to a left-wing group which, apart from Odlum, included Dr. Ralph Gonsalves, Rosie Douglas and Tim Hector.
Known as "Brother George" to his supporters, Odlum died on 28 September 2003 of pancreatic cancer. He was survived by three daughters, three sons, an adopted daughter and several brothers and sisters. He was also father-in-law of Pan-African activitist and filmmaker Owen 'Alik Shahadah.
The debating chamber of the University of Bristol Union student council has been renamed the George Odlum Room in the memory of "Brother George".