Hmm, that was confusing enough.. I explained this problem once to someone or the other, so even though it may be beat into the ground I'll go ahead and post it on the off chance that someone cares - at least the person I wrote it for seemed entirely satisfied with it.
I'll call the gods T, F and R and their postitions A, B and C.
First, we need to deal with the language barrier. We do this by tacking on an "iff da means yes", "iff" meaning "if and only if" i.e. true if both are true or both are false, false otherwise. Thus, when asked "X iff da means yes", T would answer:
X is true:
Da means yes: da (both true, so da as in yes)
Da means no: da (one true, one false, hence da as in no. Meanings switched though, see)
X is false:
Da means yes: ja (one true one false, da as in yes)
Da means no: ja (both false, ja as in yes)
As you notice, if the god answers da, same as in the iff statement, then that means yes, ja means no. Da and ja could be switched in the entire above agrument, of course. You can now consider this abstract, a black box if you will, you no longer need to worry about the language barrier. Just tack on "iff da means yes" and compare your answer per above.
Second, we have F, who lies. We get past this the same way by adding "iff you are T". For "X iff you are T":
X is true:
T says: true (both true)
F says: true (one is true (X) and one is false (being T), thus the honest answer is false. However, F lies, so true)
X is false:
T says: false (one false one true)
F says: false (both are false, but again, he lies and says false)
With the language barrier they will obviously report their "true" and "false" via that, but you cleaverly don't care since you're already past that.
Thus, asking T or F "X iff you are T iff da means yes" will give you a da on true and a ja on false, regardless of what da/ja means and regardless of it it's T or F talking. Again, you can now quit worrying about this. If you can't, reread it until you can before moving on - because you won't want to worry about it later.
Ask A, per above format, "Is B R iff da means yes iff you are T?". If A is T or F, they will give you a solid answer, da if B is R, ja if C is R. Either way, you have now found a non-R god, which you can procceed with. If A is in fact R, he will randomly and sneakily finger B or C as R. It doesn't really matter, however, because *neither* of them are (on account of the whole A being R business) so which ever one he manages to trick you into will in fact be fine. So long as you don't draw any conclusions about A (we still have no clue who he is) or anything else, you're fine.
For your second question, ask the god that you have now decided isn't R something you know, dropping the "iff you are T" but still using the "iff da means yes", for instance "Do I exist iff da means yes?". The language barrier killer is still in effect, so you'll get da for yes, ja for no regardless of their actual meaning, but the T/F filter is gone. Thus, Da means you are speaking to T, Ja means you're speaking to F.
Last question, ask about one of the other two "Is A R iff da menas yes?" for instance. You can tack on the "iff you are T" if you wish (why should us humans do all the work) or just reverse the answer if your speaking to F. Either way, you now know the identity of A, and by elimination the other of B and C (depending on whom you've already managed to secure earlier).
In case the question "Is B R iff da means yes iff you are T?" bothers you, I will go ahead and truth table it. I'll call the answer W and "da means yes" Y. R gets extra lines because he can give two answers.
Y A B C W Implicated as not-R
t T F R ja B
t T R F da C
t F T R ja B
t F R T da C
t R T F da B
t R T F ja C
t R F T da B
t R F T ja C
f T F R ja B
f T R F da C
f F T R ja B
f F R T da C
f R T F da B
f R T F ja C
f R F T da B
f R F T ja C
Those are the only 16 possible routes (6 god posistions w/ R giving two possible answers in the two cases where he speaks, two options for da/ja), nothing else can possibly happen. As you can see, in no case is someone implicated as not being R without, in fact, not being R. It's mostly downhill from there, just check which god you're speaking to, then find out about the other two.
[EDIT] Realized I should probably white text it since it's kind of a spoiler if you'd like to solve it. Changed the truth table to Courier, forgot that the first time around.
it goes like this.
