Is there any hypothetical, theoretical, or even vaguely plausible way for an intelligent being in one world to gain information about the other worlds in the MWI? Interference takes place constantly between particles in our world and other worlds; is there any way to for this interference to be turned into communication or at least advanced speculation about the other worlds?

I don't know of any models that propose a mechanism for such a communication (assuming you mean actually sending messages back and forth). A model like that would move the MWI from the realm of interpretations back into something testable. It would be way cool, of course, but don't hold your breath :)