It is more conversational than formal; also, it's a much stronger form of disagreement than just saying "I disagree."

No, don't use 'it is way off base' in a formal speaking test. It is both very informal and much stronger response than "I disagree". In saying 'it is way off-base' you are saying to the speaker they are WRONG and you are being somewhat critical as well. This is a lot different to simply saying, 'I disagree'.

many thanks, and I won't let my students use it in response to a question of the TOEFL test

No, they don't mean the same thing. To say something is "way off base" means that it is based on very mistaken beliefs. For example, "yes, the teacher is strict, but calling him evil is way off base." The speaker thinks that to say "the teacher is evil," is a mistaken belief, not just one they disagree with. It is not offensive, but I would not use it in a formal setting because it is not a precise way of speaking. However, if you did use it formally, that wouldn't be way off base ;)