Vou roubar descaradamente a Memória Alfa :
Among the parties involved was the Eastern Coalition (also referred to as "the ECON"), whose direct attacks included those against the United States of America. (Star Trek: First Contact) In 2026, at the start of the war, Colonel Phillip Green led a faction of eco-terrorists that was responsible for the loss of 37 million lives. (TOS: "Bread and Circuses", "The Savage Curtain"; ENT: "In a Mirror, Darkly, Part II")
O material não-canônico (livros) é elaborado. De Memória Beta :
One side was composed of the United States and the European Union; the other side was an alliance known as the Eastern Coalition.
The detonation of nuclear weapons over cities such as London, New York City, Tel Aviv, Jerusalem, Mecca, Riyadh, Karachi, and New Delhi killed nearly half a billion people instantly.
During fighting in Paris during the war, the Eiffel Tower was destroyed. (DS9 novel: Trapped in Time)
Então, foi EUA, UE (obviamente novo no material desde a era de Roddenberry) - incluindo pelo menos o Reino Unido e a França, a Índia e Israel, todos envolvidos de um lado.
Por favor, note que simplesmente não há tantos detalhes conhecidos sobre a Terceira Guerra Mundial em Star Trek:
... very few details have been presented in Star Trek on World War III. In 1996, this event received a Trekker's Choice Award for the 'Oft Heard but Never Seen' Award, as being "the favorite historical moment only alluded to in Star Trek."