On Retcons and Alternate Histories
The thing about the Beetleverse canon is that it's a superhero comic parody, and often breaks the fourth wall. In the interest of avoiding canon-puncturing in-game, this translates to a meta setup wherein retconning is a frequent occurrence, and some of the characters are aware of it (partly based on their intelligence, but also based on the overarching Roger Rabbit rule, where whatever is funniest is what happens, however improbable).
For instance, in the summer of 2008, during the Evilcratic presidential campaign arc, Squirrel was retconned to be six years older, to have grown up with the circus, to have the original first name of Joe, and to be able to fly without the rocket-belt. Aside from the changes that his new origin brought to his personality and interests, being closer to Queen Faraday's age when they first met changed their relationship as well, and that's just one outward ripple from one change.
This is why he has no one single origin story. Just about all the stories he can come up with were true at one point, and sometimes they run together in his head. (It's crowded in there, with all those squirrel-thoughts.)
From a meta perspective, the internal rules of the universe behave like a comic book would. Squirrel is generally always around the same age, and story arcs are generally taken to their most extreme conclusions before being cleared away so the stage can be set for the next story. Some things may stay the same, but they don't automatically have to. Squirrel is aware of the lack of continuity, and has been known to gripe about how unstable his world is, but ultimately he can't escape it. Nothing is permanent, and as long as he is only the archrival of the protagonist and not the star in his own right, the changes that happen aren't necessarily in relation to his own life and story, but rather to suit the needs of what's going on in the Beetle's story arc. No wonder he's resentful.
Another development is the alternate former selves. There was a brief storyline in the relaunch of the original comic canon where the Beetle gets pulled through time and meets his Golden and Bronze Age selves, and then his 1980s self, and the Squirrel is referenced in there (in the Bronze Age, where it is said that Bronze Age Beetle stopped fighting Squirrel and went off on his motorcycle to look for Japanese America). From this we get, among others, Golden Age Squirrel (the non-mutant, WWII Texan airman with a pet squirrel referenced in that retcon story earlier) and Bronze Age Squirrel (the not-funny-at-all, dark and gritty shapeshifter son of a trickster god and a shamaness, who is basically an ecoterrorist antihero and cult leader). In Squirrel's meta-story, he comes from WWII-era comic books, representing America as the Beetle represented Japan.
Multifacet, on the other hand, comes from the campy and reactionary impulses of the '60s. A juvenile delinquent who was thrown into radioactive ice cream and mutated into the tripolar Neapolitan Man--why, he probably drives around in his armed and armored ice cream truck, dispensing psychedelic ice cream to formerly wholesome suburban teenagers and luring them into his crazy world of substance abuse and armed robbery. Add to that his sexually liberated and therefore dangerous girlfriend Spandexwoman, and you can see why they'd be supervillains--corrupting today's youth! He hasn't changed as much as Squirrel has; in that meta way, the long stretches of time he has spent in prison represent the time when his 'comic book' would not have been published, but his recent release from prison (and pardoning by the Doe-Faraday administration) paves the way for his own (imaginary) return to the villain world as the archrival of an (imaginary) introspective Goth superheroine. Hey, the better your comic series does, the more stable your corner of the world is.
So that's that. :D They're not AU characters so much as they are prior versions of the same character--part canonical, part a logical development of how things work in canon. The world around them may change, along with some of their details, but the heart and idiom of the character are always the same. Feel free to ping with any questions.