American-English speaker here, and I'll give you the best explanation that I can. Though, mind you, it'll be merely from experience. In other words, I don't really have any textual support (like official language books and what have you).
First things first: "Be that as it may" is somewhat formal--to my ears, at least--and that may be the very reason you hear more foreign speakers saying it. I don't know how it is in other countries, but here, when we learn German, we learn Hochdeutsch. Therefore, when we speak, it probably sounds somewhat formal because we've just simply learned it that way. I'd imagine it's no different for learners of English, too. That aside, "Be that as it may"--I would say--is a bit different from "in any case" in that it refers to just one "case." Perhaps an example would help...
Person A: "No one you know will be there, so I don't know if you'll enjoy yourself."
Person B: "Be that as it may, I don't want to sit around all night, so I'm coming with you."
Ok, so even in the case that Person B will know no one at the party, he/she will still come. However, that doesn't mean the person would come almost no matter what...
Person A: "Oh wait! Your ex-girlfriend will be there!"
Person B: "Her?! Well, I'm not coming now!"
Now, "in any case" or "whatever the case" would encompass all these possibilities...
Person A: "No one you know will be there. Oh wait! Your ex-girlfriend might!"
Person B: "Well, whatever the case, I'm coming."
Now, anymore, "anyway"--or "anyways" as it is often said here in the US (though incorrect)--is more of a transition in speech than anything else. So, if person A is talking on and on, and Person B is kind of zoning out, then you might hear a response like this...
"Ya, that really sucks. Well, anyway(s), I've got to get going. Talk to you later."
In the above example, you can see that "anyway" carries a very similar definition as "in any case," in that the person is saying, "In any case of your current situation, I have to go." Nonetheless, you will almost always here "anyway(s)" used in this situation (in America) rather than the other ones.
Well, anyway (<see, told ya =D), I don't have much more to say. Hope that helps!