To be off the wall is to be strange, wacky or unusual, and in this context the person answering the question did something that was unusual.
Consider the statement "Her favorite random moments began when she asked a question and it was answered with something unusual or unexpected like, miss williams, did you know that my brother got sick last night?". Based on this "Her favorite random moments began when she asked a question and it was answered with something off the wall like, miss williams, did you know that my brother got sick last night?" a true statement? Yes, no, or I don't know?