"Out of it were birthed crackling dust and fearsome time. It were full-on winter, and Mr. Dead chasing 'em all."
— The Tell of Captain Walker
The Pox-eclipse (derived from "apocalypse") was the name that The Lost Tribe gave to the nuclear exchange that marked the end of oil-based civilization.
According to Dr. Dealgood, civilization ended with a war that was "damn near the death of us all." The Lost Tribe represent this war in their cave paintings with a nuclear mushroom cloud. The exact date of the event is not known. According to George MIller, in the original timeline the nuclear exchange happened after the events of Mad Max 2, but according to the 2015 Mad Max: Fury Road prequel comic books, the war occurs after Max Rockatansky defeats the Toecutter's road-gang and disappears into the Outback, but prior to the events of The Road Warrior.
It would seem that Australia was mostly spared from the nuclear conflict, although it is possible that some of the larger cities were targeted. Sydney seems to have been hit with at least one nuclear weapon.
By this time, road gang activity had become so familiar that children might refer to any group of people as a "gang." Nuclear winter and fallout contamination followed shortly after.