Answer: Yes, there is a complete strategy with 3 questions.
Central idea (control motto)
For any $P$ proposition, use the question:
"If I asked you '$P$', would you answer 'ha'?"
If the interrogated god is not Random, this form has two advantages at the same time:
- neutralizes the lie (Truth/Falsehood are aligned),
- neutralizes the unknown translation of
ja/da.
Result: the god answers ja if and only if $P$ is true.
Step 1: Make a non-random god
Q1 to $A$:
"If I asked you 'Is $B$ Random?', would you answer 'ha'?"
Defines:
- if Q1 =
ja, take $X=C$;
- if Q1 =
da, take $X=B$.
Why does it work?
- If $A$ is not Random, Q1 correctly reports "$B$ is Random" and you choose the other one, which is not Random.
- If $A$ is Random, then $B$ and $C$ are not Random; Whichever one you choose ($B$ or $C$), $X$ remains non-random.
Conclusion of step 1: $X$ is guaranteed True or False.
Step 2: Decide if $A$ is Random
Q2 to $X$:> "If I asked you 'Is $A$ Random?', would you answer 'ha'?"
- If Q2 =
ja, then $A$ is Random.
- If Q2 =
da, then $A$ is not Random.
Step 3: separate Truth and Falsehood
- If Q2 =
ja ($A$ already identified as Random):
Q3 question to $X$:
"If I asked you 'Are you True?', would you answer 'ha'?"
With this you distinguish whether $X$ is True or False, and the third is determined.
- If Q2 =
da ($A$ is not Random):
Q3 question to $X$:
"If I asked you '$A$ is True?', would you answer 'ha'?"
That determines whether $A$ is True or False and, by discarding it along with Q1, determines the three gods.
Methodological conclusion
The strategy separates the problem into three tasks: (i) find a non-random, (ii) locate Random, (iii) label True/Falsehood. With 3 answers you obtain unique identification.