Shift work can definitely wreak havoc on the rest of your life!
I would say exercise on your off days from work whenever you typically wake up for the day. That way you are consistent in the 'time of day' and the days you exercise. As far as food - small meals throughout the day (and night) will help to fuel you, so don't be afraid of eating regularly. Just be sure you are eating planned meals with healthy options and you're not eating out of boredom or because you are trying to stay awake.