Organ was born in Bulli, New South Wales. His mother was a hospital domestic and his father was a brickworker. He studied geology at the University of Wollongong and completed a post-graduate diploma in archive administration at the University of New South Wales, where he subsequently took up a post as an archivist. He has been employed at the University of Wollongong library, as an archivist (1996–2002) and, as of 5 May 2013, manager, repository services.
Three months prior to the Cunningham by-election, he unsuccessfully contested the local government election for the lord mayorship of Wollongong.
He has four children, Andrew (b. 1991), Kyle (b. 1993), India (b. 2008) and Emma (b. 2011).
The federal division of Cunningham has been a safe Labor seat since its creation in 1949. On 16 August 2002, the sitting member, Dr. Stephen Martin, unexpectedly resigned, causing a by-election.
The ALP preselected a TAFE teacher, Sharon Bird, by decision of the party executive rather than the usual rank-and-file nomination procedure, and the Liberal party opted not to contest the by-election.
Organ was endorsed by the South Coast Labour Council and received strong preference flows from two popular independent candidates, David Moulds and Peter Wilson. He gained 23% of the primary vote and 52% after allocation of preferences, defeating Bird and becoming the first Green elected to the House of Representatives, at the same time making Cunningham a marginal seat.
During his term, he was one of three Greens federal parliamentarians (with Senator Bob Brown and Senator Kerry Nettle).
Organ ran for a full term in the 2004 general election. While he was eliminated on the ninth count, his preferences flowed overwhelmingly to Bird, allowing her to win.
He was preselected as the Greens candidate for Cunningham in the 2007 federal election, but failed to regain the seat from Bird.
He contested the position of Lord Mayor of Wollongong City Council for a second time in September 2011.
In his first speech, Organ credited his win to community opposition to a planned development by the Stockland Trust Group at Sandon Point. The campaign included a tent embassy by the local Kuradji nation, and a community blockade of around 300 people which was confronted by a force of around sixty police officers and police dogs. Organ said that the development was inappropriate, threatened European and Indigenous cultural heritage, threatened wetlands and a green corridor.
Organ supports free tertiary education and opposes the privatisation of public utilities like Telstra, as well as what he calls "two decades of Canberra's obsession with economic rationalism".
In his first speech, Organ condemned the Iraq War as unjust, in breach of United Nations resolutions, and likely to lead to higher risks of terrorism.
Organ co-authored a Greens policy on Tibet, which supported the right of Tibetans to self-determination and the Dalai Lama's Middle Way approach. He participated to the Save Tibet Asia Pacific Forum in Tokyo 1 –3 July 2008.