I'm currently on mobile, so I'll just add some quick response. I'll make more sense when I'm back on my computer, haha.

So I think the difference in technology would only really be an issue in the medieval fantasy world, but since it is a world wherein magic (possibly) exists, it shouldn't be too farfetched to believe modern/futuristic technology just don't work. Maybe there's magical particles in the air that interfere with them? Or a barrier around the entire world that prevents them from working? It might get difficult to be consistent if all resources from other worlds aren't allowed to exist/just get vaporized in a new world, like you said. 

EDIT:
As for what the baddies can do, we could go classic route and maybe have gems/orbs/any sort of power source/parts of the weapon scattered all over the different worlds, so no one person can use a powerful weapon. Of course, the baddies will want all three of them, so they travel between worlds to get their hands on them.