I thought of it a lot like taking the GREs. Be hydrated, bring a snack, get good rest the week before (melatonin is great if you're having difficulty sleeping), and don't stress yourself out trying to cram last minute (night before/morning of) because it likely will not make a difference.
One thing that really helped me on my last interview was getting to know the graduate students at the dinner before. It made the actual interview day much less stressful, and we all know that interviewing is mentally exhausting enough without being extremely anxious/stressed all day. So just prep before and once you're there, focus your energy on getting to know the program, students, and faculty! You're trying to assess their fit with you as much as they're assessing your fit with them, which is hard to do if you're trying to memorize questions or facts for your interview.
If you need to take a personal day or two off of work/school, DO IT! Self-care during this process is important. Plus, think of how much time and effort you've put into this. The interview is for your potential future career, and I'd hope your professors/boss would get the importance... but if they don't I'd still say take off a day (just try to make sure it's not a crazy day at the office/in your class if possible, maybe a day where there's not a whole lot going on and you can easily make up the work if needed).
As far as avoiding illness, I have been drinking Emergen-C every other day (if not every day) to avoid catching a bug going around my office... so far I'm the only one who hasn't gotten sick! *fingers crossed* I think exhaustion by the end of the interview day is unavoidable though unless you're literally a robot. On the bright side, it's a long day for everyone so you definitely won't be the only one who's tired.
Good luck!