How does one phrase a request for a Rabbi's opinion on a halachic matter so as not to receive a psak? Are there multiple acceptable expressions?
I agree with Isaac Moses' answer; clear and direct communication is your best bet.
An additional suggestion: say that you're seeking an "eitzah" (עצה, lit. "advice"). In some circles (e.g. yeshiva orthodox), this is usually understood as a request for advice or direction, without the weight of a formal psak.
But again, to reiterate that first point: clear and direct communication is your best bet. Using this phrasing will work best when you are sure that the message will be received in the way that you intended it. And it might not be a bad idea to confirm that the word "eitzah" means, to your rabbi, what you think it means.