Michael's answers seem to be on the mark, so I'll just give a response based on artificial dialogues in Question/Answer form:
1. I think they will.
Q: Do you think John and Sarah will come to the party tonight?
A: Yes, I think they will.
Reasoning: The party is definitely happening, and the person answering the question believes that John and Sarah both are able to attend the party, and will choose to do so.
2. I think they would.
Q: If I had a party tonight, will John and Sarah come?
A: Yes, I think they would.
Reasoning: The party isn't definite, but the person answering thinks that if there was a party, John and Sarah would choose to attend.
3./4. I think they may/might.
Q: Will John and Sarah come to my party tonight? // If I had a party, would John and Sarah come?
A: I think they may/might.
Reasoning: May/might are used when the person has the capability to do something, but their intention is unclear. This is very similar to saying "I think they will come." However, "will" implies a greater likelihood than "may/might."
5. I think they can.
Q: Are John and Sarah able to come to the party?
A: Yes, I think they can.
Reasoning: This assumes that the party is definitely happening, and asks whether the subject is able to join. This doesn't suggest anything about intention - simply, can they, or can they not?
6. I think they could.
Q: If I had a party, would John and Sarah be able to make it?
A: Yes, I think they could.
Reasoning: In this situation, the party might happen or might not happen. The question is asking whether the subject could attend if they party does happen.