NSE's official site http://web.mit.edu/nse/education/grad/phd.html contains the most up-to-date information concerning curriculum and exams.

Oral exam (a couple of days to 2 weeks after the written exams):

• Upcoming: Feb 3-12, 2014
• 1.5 hours for answering the 1st question (prepared question), another 1.5 hours for the 2nd (mandatory question).
• First question will be given to you a week before your oral exam date, and it is specific to your chosen sub-field (e.g., in fission there are reactor physics, thermal hydraulics, material etc). You are allowed to do whatever research you need as long as you don't get help from anyone else, and generally you can bring 3 slides to the oral exam (whether you can bring in notes and backup slides etc differ from area to area, so check with your professor!)
• Second question will be given to you on the spot, and you have 5 minutes to read the problem and prepare an answer. All fission students get the same question (and same apply for fusion and NST). For fission, it is typically a general reactor-related question.