Born in Tipperary, in Ireland, O'Dwyer has lived in Israel since 1989 and become one of the most popular writers for The Jerusalem Post and other English language publications. After a training in publishing, he left Ireland in 1966 and has been abroad ever since.
In 1977, after a 10-year career as an aircrew officer on the British Royal Air Force's nuclear strike Vulcans, he emigrated to Cyprus to start a new career as writer and journalist. He worked as military and political analyst for the Arab Press Service in Nicosia and was later appointed editor of The Cyprus Mail English-language newspaper. As a freelance correspondent, he reported for the BBC World Service and wrote the Cyprus section of the Encyclopedia Britannica Yearbook for nine years.
In 1982 he opened the first permanent office of Reuters News Agency in Nicosia and was Reuters bureau chief in Cyprus for four years. He worked in Cairo and Amman and spent six months in Beirut. In 1986 he went to Bahrain as a sub-editor at Reuters Middle East headquarters. He was sent to Dubai to cover the last six months of the Iran-Iraq shipping war.
In 1989 he moved to Israel as news editor of a new newspaper, The Nation. The newspaper failed and he moved to The Jerusalem Post as foreign editor. In 1997 he revived the Post's Column One, made famous in the 1940s and 50s by David Courtney.
He appears, according to an article he wrote in Ha'aretz in October 2002, to have become an Israeli citizen and is still (2011) living in Israel.