(Updated with more possible deities)
You live on an island ruled by three deities who will answer yes/no questions for the inhabitants. They're overly obsessed with never appearing in the same form twice, so you never know which one is which when you show up at the temple. Truth always tells the truth. Liar always lies.
Since you're tired of chronically playing games of Knights and Knaves every time you've got a trivia question you want answered, you decide to thin down the numbers: The ancient scrolls or some such say that if a deity is unable to produce a yes/no answer due to a paradox, his head will explode.
So, what questions can you ask to identify each deity (fairly easy, no points), kill a specific deity which will not harm the other two (2 points), or a question that'll kill two deities without harming another (5 points). Minus infinity points for a question that'll kill all three, since that'll arouse the attention of the Hounds of Tindalos, who'll rip you to shreds, or whatever they're supposed to do. All I know is that I like their plush.
Alternate deities to replace Random/Whimsy, to possibly expand the challenge:
Chaos: Switches randomly between honesty and lying.
Alternator: Switches between telling the truth and lying with each question. First answer is random.
Yes-Man: If Truth and Liar give the same answer, he will give the same answer as well. If Truth and Liar give different answers, he will lie.
Ragnarok: If Truth's and Liar's heads explode, he will answer to cause his head to explode. If that option isn't available, he tells the truth.