A helpful task in this is discerning, at the very least, a non-random god which we can ask two questions to find other gods, and therefore find the third by elimination. So, we need to find in one question a non-random god, though it doesn't matter which.
In this, we're going to ask 'B'. It doesn't quite matter which, but just for arguments/examples sake, i'm going to ask B.
If we ask him a question concerning one of the other two to decide which is not random, and B is random, it doesn't matter which direction he points us in, as both will point us to a non-random person.
We therefore need a question that makes the truth teller point us to the liar, and the liar point us to the truth teller. For this, we just need a 'If I asked you X, would you say Y'. We don't want the random, so we use 'If I asked you is <A or C> random, would you say <Ja or Da>"
Say we use A and Ja, and Ja is true. A is the Liar, B is the Truth Teller, and C is random. We ask B, the truth teller, whether he would say A is random. He would answer da, no. If he answers da, we move to A as A is a non-random character. If A was Random, B the truth teller and C Random, he would say ja, and so we go to C. If A was the Truth teller, B was the Liar and C random, the liar would say da, and so we move to A. If A was Random, B the Liar and C the truth teller, he would say ja, and so we go to C.
If he says Ja, we go to C for the final two questions (Of which there are many), and if he says Da we go to A.
It works for the reverse, So we're using A again, and Ja, but Ja is false this time. A is the Liar, B is the truth teller and C is random. B, the truth teller, is asked if A is random, which he isn't, therefore A would say Ja, false. If asked, would he say ja, he would say da, yes he would say ja. As we said earlier, if he says da, we go to A, which is the liar. It works for the rest.
So, we ask B "If I asked you is A random, would you say 'Da'", and we then move our questions to A if he says da, and C if he says ja.
Next, finding one of the gods. We need to ask him a question about what he would answer, as this causes the truth teller and liar to always say either ja or da, depending which is true. In this case "If I asked you whether you were the <Truth teller or liar>, would you say <ja or da>. Lets use Truth teller and Ja. We ask the truth teller, he always says ja (Either ja is true, and so he would answer true to yes he is the truth teller, or ja is false, and he would answer no when asked would he say that he isn't the truth teller). The reverse goes for the liar, who says da.
So, the second question could be "If I asked you 'If I asked you 'Are you the truth teller', would you say ja?", and we now know whether he is the truth teller or the liar.
The last question can work in very much the same way.
"If I asked you 'Is B random", would you say ja?". If B is random, the truth teller says 'true', and so says ja if ja is true and ja if da is true. The liar says ja if ja is true, and ja if da is true. If B isn't random, the truth teller says Da if ja is true, and da if da is true, and the liar says da if ja is true, and da if da is true.
If he says ja, B is random. If he says da, the person who hasn't answered a question is random. The third is found by elimination.
1. Ask B "If I asked you is A random, would you say 'Da'", and we then move our questions to A if he says da, and C if he says ja.
2. "If I asked you 'If I asked you 'Are you the truth teller', would you say ja?" if he says Ja, he is the truth teller, Da, he is the liar.
3. "If I asked you 'Is B random", would you say ja?" If he says ja, B is random, if he says da, the unspoken-to-god is random.