For example, should it be: A) Ask the Science, Math, or Art teachers. or B) Ask the Science, Math, or Art teacher. ?
Technically, you would only use "teacher" if there was one teacher for each of the subjects Science, Math(s), and Art. The choice is being presented as exclusive (science teacher OR math teacher OR art teacher), so you'd only be asking one teacher in the special case where each subject only has one teacher.
If more than one person teaches any one or more of those subjects, you would use the word "teachers".
But in the real world, even in the case that there is only one teacher for each subject, you are not likely to be faulted for using "teachers".