There are subtle differences of meaning.
I wish I knew what he would do in this case.
You admire his judgment. He is wise. If you knew what he would do, you would probably imitate him.
I wish I knew what he will do in this case.
You may likely be in conflict or negotiation with him. You are worrying about what he might do in the future.
I wish I knew what he is going to do in this case.
Same as immediately above.
I wish I knew what he was going to do in this case.
The matter is past, settled. We all know how it came out in the end. The speaker is asking speculatively how things might have ended differently if his intentions had been known.
Student or Learner