Okay, I'm new to Erfworld theory, so please correct any and all mistakes that I've made based on what's canon, including what's most likely canon.
But otherwise here goes:
Judy = Judy Garland, obviously.
EfBaum = the author of Wizard of Oz. I can only assume that someone will eventually drop the Efbaum. I don't think Rich can resist
Charlie = The Wizard. The Wizard is a Stupidworld word: otherwise he'd be the Caster. In the same way that "Tool" became a real Erfworld word, I bet something similar happened when Charlie (if that's his real name) came through to Erfworld.
Arkendish = Thinkamancy.
Arkenpliers = Croakamancy
Arkenhammer = Changeamancy (because in addition to the other "for" arguments, I believe that revolution ie, usurping the throne from the Royal lineage which is very well entrenched as a tradition in Erfworld might be powerful enough---it is literally impossible to go against your leader; but Charlie did--albeit it from arm's length using Gobwins--but even to orchestrate that would have required treasonous action. Though perhaps he got around it by thinking replacing Saline IV was better for the side. Ie, he shifted his loyalty to the side, not the king. But I'm not sure that's possible...if it is, I think it constitutes a change in and of itself.) Also, as an aside, I'm pretty sure that there are Hitler parallels that don't appear on the wiki entry for Stanley, insofar as Hitler started out as a nothing infantryman in WWI and eventually became Overlord of Germany etc etc. Small, diminuative, micro-managing, extremely punitive towards all failure except his own, HORRIBLE tactician, etc etc etc. WHICH, if that's accurate, can be further (shaky) evidence for the power of the Arkenhammer: Hitler was defeated. Stanley pulled a rabbit out of his ass.
NEXT: The 4th Arkentool: No idea, but I'm reasonably sure that Olive Branch has it or had it. I'm guessing, if it has to be fatemancy (which hasn't been proven) I would suggest Signamancy since that's the Hippiemancy class of Fate magic. This assumes, of course, that Olive Branch is still alive. If not, then I would suggest the fate that drove Wanda to attain the 'pliers allowed Olive to be as powerful as she needed to be; cf. Beren breaking Luthien's girdle because the power of his doom was stronger than the power of Melian.
WHY are the arkentools what they are? I can't see a parallel between pliers and uncroaking something. Nor can I see a connection between a dish and thinking, unless it be the similarities of brainwaves to radio waves? I do not propose that the tools are bound to magic classes, rather, I believe they "attune" to the class of magic that's the natural domain of the person who's destined to wield it. Furthermore, even after being so attuned, they can still exhibit other types of magic even outside of that class; for example, the shockamancy of the arkenhammer, though in order to feel completely comfortable saying it, I'd REALLY like to see another tool explicitly and flagrantly do something outside of its attuned magic class.
But let's get back to the Stupidworlders in Erfworld: We have no evidence that they age while in Erfworld. While Judy Garland looks a little worse for wear; that may be as much a product of the prolonged drug use that she's been doing since god knows when. I think it's safe to say that something weird goes on with the passage of Time: If the Titans are in fact Fat Elvis, then that would date the creation of Erfworld somewhere in the late 1970's. However, Judy Garland acted in the Wizard of Oz in 1939.
But this leads me to believe that this is in fact some sort of trip--perhaps the first segments of the Comic (ie, the game with other people in it who witness Parson's departure) are part of the hallucination? In the same way that Dorothy apparently dreamed a tornado blew her away (though apparently, one actually did, since she's still in Erfworld), at least according to the "real world" storyline of the Wizard of Oz. Assuming this is a dream-like state, then there may very well be those types of people who would prefer it to the real world, Charlie being one of them. Parson may yet decide not to return given the opportunity.