How should a teacher approach a student with distractingly strong perfume? How might a professor approach a student who comes to class and/or office hours wearing perfume or cologne that is distractingly or overwhelmingly powerful?

Certainly, different people have different thresholds for this sort of thing. Lets say that in this case it is unclear the extent to which this is distracting other students in class but it is clear to the teacher that it is strong enough to distract the teacher. Of course, it might be affecting other students as well.
I might ask quietly and privately to speak to the student immediately after class. At that point, when no one else is present, I would politely say, "I am sensitive to the strength of your perfume". After that, I would let the conversation unfold. When the student would be defensive, I would just politely repeat the one statement "I am sensitive to the strength of your perfume". I might add "This is a health-related issue for me, as much as an allergy might be. It could eventually affect how I could continue to teach in the class". I would NOT ask or even suggest the student should NOT wear the perfume or take any action. I would hope the student would volunteer that step.