He served as a staff member of the Rockefeller Foundation, and director of the Foundation's laboratory in Brazil, as a research fellow at the Yale Arbovirus Research Unit, was head of the Arbovirus Laboratory for the New York State Health Department, and worked for the Centers for Disease Control.

After retirement in 2007, he continued as a consultant and professor at the Institute of Medical Biochemistry in Rio de Janeiro, Brazil, where he had worked since 1998.

Woodall's emails concluded with a quote from the Calvin and Hobbes cartoon, "God put me on this earth to accomplish a certain number of things.

After graduating from the University of Cambridge, he obtained a PhD in virology and entomology at the London School of Hygiene and Tropical Medicine.

Woodall had over 30 years of experience isolating and characterizing viruses from humans, wildlife and arboviral vectors (mosquitoes, ticks) in Africa, the Caribbean and Latin America.

The disease was officially named the Crimean–Congo hemorrhagic fever virus at the insistence of the Soviets, despite violation of the principle of priority of publication, an event that Woodall noted was maybe the only instance of viral nomenclature overruled by politics and the Cold War.

[5] At the Entebbe Lab, Woodall and a colleague made the first isolation of the o'nyong'nyong virus in 1959 during a large outbreak of a disease that appeared initially to be either dengue or chikungunya fever.

[12] Woodall then moved to the Foundation's Yale Arbovirus Research Unit, where he continued work with the data gathered in Brazil.

At WHO he first became involved in the control of chemical and biological weapons, cofounding Task Force Scorpio, a United Nations rapid response team formed during the first Gulf War and then disbanded.

[22] Woodall published numerous articles in peer-reviewed scientific journals, wrote for the lay press, edited newsletters, and appeared on TV.