The Weasel Way to Win:
On the difficult side, it might be hard to come up with questions in which the proper answer is, quote, "Yes or no". (As opposed to "yes" or "no", see?)
On the easy side, since he's not obligated to answer any of our questions properly, unless he cuts out his tongue he 'can' answer any of our questions with "yes or no". Even if he chooses not to, he totally could have, so they'd count. (For example: Sheogarath answering "What is the air-speed velocity of an unladen swallow?" with "Yes or no" is a possibility, so that question would count as asking one in which he can answer that way.)
Given the latter, perhaps just asking him questions in which we're interested in the answer Sheogarath will give, regardless of its truthfulness is the best strategy. Asking him questions interesting enough that he'd consider giving us a proper answer would be key.
The Non-Weasel Way to Win:
Of course, for those not interested in that kind of rules-lawyering, who want to treat this merely as a game in which we win if we ask Sheogarath five consecutive yes/no questions three times:
-Note each round is five questions. Asking him two non-binary questions, then five consecutive binary questions, then three non-binary seems like it either results in two rounds won for Sheogarath (in that round one only had three binary questions and round two had two binary questions) or one round for Sheogarath and one for Michael. (in that round one ended without Michael finishing a string of five binary questions, but he automatically wins in the middle of round two because Sheogarath never said you could only win a round at the end.)
-Note we can tie with Sheogarath by winning two of the four rounds. If we do, neither player wins. No castling for Sheo, no 'satisfaction for a job well done' for us. We may actually want to actively try to tie, if we assume 'satisfaction' is somehow related to 'resting in peace'.
-Note that we aren't limited to yes/no questions - we just need to ask enough to win/tie, probably in the right grouping. That means we can safely ask him five or ten (depending on the desired outcome) non-yes/no questions if we're curious about the answers he might give.