I answered that my biggest strength and weakness was actually the same thing - my emotions. I answered that I was going to help the company grow by working my way up in to human resources and helping find great people to work on an already awesome team. Two and a half years later, I have done so and couldn't imagine working anywhere else. I love what I do every day and come to work singing. My fellow team mates do the same thing.
Remain calm and try to gauge the situation, always pointing out you're willing to help but not to the point where you jeopardize your other tasks. If they prove to be too difficult, then seek advice from higher.
I responded by pointing out that in my military service and subsequent civilian jobs, I worked all manner of shifts and hours. If something came up on short notice, all I need is enough time to clean up and get dressed and I would be there.
For the most part, I have healthy stress management skills. If there is a situation or circumstance that stresses me significantly beyond my ability to cope, I would seek out my immediate supervisors or colleagues for tips.
The interviewer was interested in breath of experience rather than specific technical skill. Unix work with scheduling and XML skills are necessary, but not heavy (the same procedures are done over and over again). Emphasis was on selling yourself through experience.