OK diplo, you didn't answer my question, but I'm going to assume that I can ask two of my questions to the same god. If so, then I have a solution.
First: I will make extensive use of "xor," and for shorthand, that's what I'll say. If the gods didn't recognize that as an English word, I would spell it out, saying, "Is it true that precisely one of p and q is true, where p is the proposition that...." etc.
Second: it turns out the language thing doesn't matter at all. If instead of the question Q, I ask (Q xor (Da means no)), then it turns out that I can act, with respect to True and False, as though Da means yes and Ja means no. So from now on, I'll just act as if they are saying yes or no, for ease.
There are six possibilities. Labeling in order ABC, these are TFR, TRF, FTR, FRT, RTF, RFT. The first question (Q1) I would ask, to A, is "Is C Random xor You False?" If the answer was Yes (Da), the remaining possibilities would be RTF, RFT, TFR, FTR. In particular, notice that I now know that B is either T or F. So now, ask Q2 "Is 2 + 2 = 4?" If he said yes, then I know I have RTF or FTR, so I now just ask B, "Is A Random?" I know I can trust his answer, so that determines everything. If the answer to Q2 is false, I know B is False, so I can just do the same but take the negative.
Similarly, if the answer to Q1 is no, then I have RTF, RFT, TRF, or FRT. This time, I know that C is either True or False, so I now do the same trick, but with him.
And that is all.