I hope that the answer does not come across as being too cynical. Others may correct me, but usually I (would) ask, "do you feel comfortable writing me a (very) strong letter of recommendation?"
On the giving side, I would ask, "do you need me to write you a strong letter of recommendation?"
I hope that is what most people did when they say they have strong letters. Your judgment of strength goes from how strong the mentoring relationship is (i.e., did I have to ask you as a student or a reference?).