I was thinking to it last nite (yes, I can "think" too!).
THREE DIFFERENT LINES - each one featuring a different "sense" of reality; each one featuring a SLIGHTLY or HEAVILY movement of the historical events, each one featuring a different "MAX".
MAD MAX
THE ROAD WARRIOR
BEYOND THUNDERDOME
According to Miller, the movies all belong to the same universe... evidence shows the opposite.
MAD MAX --------> The "big event" could have been just an ordinary energetic crisis, sort of a petroleum rise of the prices or sh*t like that. Yes, MAD MAX 1's world is an "aftermath" anyway. The sense of reality is pretty realistic here.
Society is crumbling, BUT ***DEFINITELY*** not to the point society will disappear in the following years.
Toecutter killed Max's family (as we already know) and Max killed Toecutter (as we already know).
Since then, I bet Max returned to M.F.P's headquarters, kept to be a policeman, maybe he experienced a trial, or social structures were as much lowered to the point a man is allowed to act as a vigilante without passing judgement.
No war, no nuclear exchange.
THE ROAD WARRIOR -------> Different world, different MAX ---- he's another guy, the alternative space-time continuum line version of the "MAX" we met in "MAD MAX".
This time there was a collapse of the society due to a LONG LONG WAR (no nuclear exchange).
I bet the war was still going on when Max II's family went killed - in the b/w prologue the events similar to MAD MAX 1 are easily inserted among the war events.
Max II's world is gritty, bleak, with no shortage of blood spilling.
There were never Armalite Gangs or sh*t like that, HUMUNGUS' DOGS OF WAR represented the brand-new, never-displayed-before product of the "downhill".
Max II did not ricover himself in the end. Granted, he "salvaged" a little bit of humanity for himself, but he's doomed to wander in a violent, destructive Wasteland for the rest of his time 'til death.
No kids, no Aunty Entity, no Thunderdome, no Master Blaster... he's doomed to scavenge and meet even worse Marauders for the rest of his f**king days.
BEYOND THUNDERDOME ---------------------> MAX III. He's more vulnerable, more agile and more tricky than the previous "Maxes". His world is far more easy, the "sense" of reality is far more cartoonish to the point a man can survive to a fireball, kids live alone in the Wasteland or sh*t like that.
I doubt Max III experienced Max II's gritty event: he's a far more "open" man, he's witty, not brutal. I don't see him like "burned-out" or even "desolate" man, neither a man who "ricovered" his humanity because he never lost it in the first place.
I bet MAX III was 21 when the NUCLEAR WAR happened, so you can suppose 24 years have passed by since then. MAX III worked on his skills along the way, in the PG-13 Wasteland. 24 years are enough for a bunch of man to build such structures like BARTERTOWN and the THUNDERDOME itself or for a buch of kids to FORGET all the "civilized" sh*t and start to believe in a new RELIGION: WALKERISM!
Sure as hell he lost his family but WAIT! Since the excerpt featuring MAX III's complaints was a sequence deleted out of the final edit of the movie, probably it never happened in Max III's life.
Now, some comparisons between the WORLDS:
MAX I - a combination between JOHN WAYNE and a VIGILANTE. Classic western world.
MAX II - the refreshed, futuristic version of the MAN WITH NO NAME. Spaghetti western world.
MAX III - A TRINITY/NOBODY (TERENCE HILL) type of guy, much more resembling "positive" models as MACGYVER and so on. Fagioli western world.
Besides, it seems to me that the ACTION SCENES displayed by each of the movies are resembling a specific "element".
MAD MAX - explosions ------> FIRE.
MAD MAX II - straight-to-the-point violence ----> EARTH.
MAD MAX III - acrobatic action a-la "circus du soleil" ------> AIR.
MAX I, MAX II and MAX III represent WATER in its different forms. Meeting FIRE, WATER disappears; it becomes SMOKE (a vanishing, totally wasted man).
Meeting EARTH, WATER becomes MUD (a brutal, dirty man).
Meeting AIR, WATER stands alone, it doesn't react (a fluid but vulnerable man).
I'm not smoking, however.

What do you think about? I challenge you to "detect" more clues about the theory in the three movies.
LAST OF THE V-8 INTERCEPTOR to anyone? In "MAD MAX 1" it was supposed to be... a PURSUIT SPECIAL.
Ah, shut up Uncle. It was a different universe.
Same for... the BRUCE SPENCE BIG QUESTION !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Sort of SERGIO LEONE's DOLLAR TRILOGY.