It's vague. In the first film, no mention of the rest of the world, IIRC. There's just the setting of society breaking down. But in that film it was still there holding on, so that there was still law enforcement, (overwhelmed, but there), and you could still go to a mechanic and buy new tires.
The second film starts with a montage explaining more--there was a war, and further breakdown etc...although nukes are not mentioned, they are implied.
All three movies are very, very different in tone. In 1, it's set in some nebulous dystopia. Max heads out into the "wasteland" of the outback at the end. 2 clarifies that the world has been undone by war. Perhaps in 1, in civilization, things are a little less scary than in the wasteland? It's like Pitch Black and Riddick, a sequel that all but reimagines the original. 2 is the spaghetti western of the series.
3 is slick Hollywood crap. It attempts to basically remake 2 on a big budget, with some 80s save the children crap tossed in. The gyro pilot returns, but it a totally different character though it's the same actor with the same copter (?!?!?!?). It has even less connection that the first two.
It's almost a reboot. Bizarre.
1 and 2 are some of the great films of sci-fi. Powerful, audacious film making. Let them be.
My understanding of the continuity is this:
Pre-Mad Max 1 -- war starts, oil crisis kicks in. Australia begins to descend into anarchy, trans-continental highway is built. In response to road gangs (usually bikers) messing with trans-continental commerce via the highway, the Main Force Patrol is created. Max Rockatansky (yes, that's his name), is a hotshot young cop working on the force who distinguishes himself early on.
Mad Max 1 -- society has continued to degrade. The MFP continues to increase its brutality in response to increased brutality by the gangs ("So long as the paperwork's clean, you can do what you like out there."). Fifi McAffee (Max's boss) wants to turn things around, but he's holding on to a world that is slowly disintegrating. Taht said, it's not at total post-apocalyptic wasteland yet. Max can still go to the shore with his wife and son. And then things go very very wrong. By the end of it, Max has abandoned being a cop and is a lone vigilante who has stepped out of society altogether...
Mad Max 2/The Road Warrior -- ....which doesn't really matter much because society pretty much goes down the tubes somewhere between MM1 and MM2. At some point, there are nuclear exchanges and oil basically disappears. Papagallo, an oil engineer, realizes this and forms a community around a refinery. Their plan is to travel to the coast (coastal regions in Australia have always been more easily inhabited). They now fight even more brutal scavenger gangs, whose ranks appear to include ex cops (possibly even ex-MFP). Max wanders into the midst of this (and eventually wanders out).
MM3/Beyond Thunderdome -- Society is just starting to rebuild in the form of Bartertown (and probably other settlements like it). the timeline is hazy as to how long after MM1 and MM2 the third film takes place, but there's a sense that the kids in the "Crack of the Earth" have been there for perhaps a generation (bearing in mind that, without the strictures of society, teenagers could've been getting pregnant and having babies). Oral history of the "pockyclipse" has been passed down and it's unlikely anyone alive among the kids actually remembers it first hand. At the end of the film, there's a sense that the kids have re-formed society in the ruins of the old cities (which were themselves apparently destroyed completely).
Anyway, that's my rough understanding of the timeline. MM3 is a far weaker film than the first two. The first one is a stunt spectacular and a slow burn of a revenge film. It's not very "sci fi" at all. More just dystopian future. The second one is far more "post apocalyptic" and is arguably THE film that created that genre, or if not created, set the standard for. Every "post apocalyptic" film since then owes its heritage to MM2. MM3 is, as has been stated, kind of just a big-budget remake of MM2 but really plays fast and loose with an already hazy continuity. It's also watered down for violence and kiddied up for We Are the World appeal. Tina Turner, however, never looked sexier.
