In order to answer the first part of this question, regarding how to tackle/handle such odd/off questions, I first need to explain what, in my experience, interviewers look for when they ask such questions.
Why They're Asked
When preparing for an interview,there are a few "golden questions" that most people prepare answers to. These are questions that are asked almost all the time, and have had papers and entire doctorate theses focused around them. Standards like "where do you see yourself in 5 years" tend to result in semi-rehearsed, or at least pre-thought-out responses. Many employers are looking for something...extra. A semi-canned response to a popular question tells an employer nothing about an interviewee's ability to adapt and think on their feet.
In most modern workplaces, sometimes, situations will arise. circumstances will come about that you can't predict. It might be a certain server spontaneously die, or even something as simple as a caller becoming aggressive and obstinate. In such cases, an employer wants to know that you could be trusted to, if not handle things perfectly, at the least keep your cool. They ask off-beat questions in interviews to judge your impromptu problem solving skills, your ability to be outside your comfort zone, and generally how easy it is to phase you. Now, to transition into actually answering such questions...
How to Answer
There is one good thing to say about these questions, there are very few wrong answers. The only way you can give a wrong answer is to give an answer that would not be appropriate in society. Things that are blatantly illegal or unethical are BAD ideas.
Indeed, other than such responses, the content of your answer doesn't matter. Rather the manner you answer is important. fumbling around, stalling for time, saying "ummm" or "ahhh" like you're at the doctor can show your interviewer that you have some trouble thinking on your feet. It also reeks of low confidence. If you're not confident in your abilities and yourself, why should a stranger be?
Speaking calmly, clearly, and succinctly is your best course of action. If I am asked a wacko question, I normally chuckle if I find the question amusing, and then I don't think too hard, I just talk. I give AN answer. Of course, I make sure to not give any sort of...unsavory answer, but within three minutes of being asked, I have given an answer to whatever question has been asked, and remained calm. Being flustered is alright, it's expected. But letting yourself be impeded by it is bad.
How to Prepare
Here is the fun part. Preparing. If you understand why these questions come up, you're halfway there! If you want practice, try paying attention to how conversations with your friends flow, how you tend not to stop, consider, and rehearse your interactions, and rather how you simply respond. It's a different mindset that many people have trouble falling into consciously. I can tell you that taking classes in improvisational theater has helped me immensely. Not only has it assisted me with interviews, but knowing how to field these weird questions has helped my public speaking, phone support, and general problem-solving skills more than any formal training or the like.