If you're hungry, it's generally a sign that you need to eat. Most people have a meal a few hours before they go to sleep, so a 2 am meal sounds like a good idea given your current sleep schedule.
You're hungry because you're not eating enough, and going running means that you're going to need more food anyway. Eat more throughout the day (when you're awake), and proper meals not just little snacky things (snacks are ok in addition to decent meals). Get up when you get up, have breakfast (even if you're not massively hungry), lunch a few hours later, dinner a few hours after that, and maybe a few snacks between. Don't worry about adhering to conventional meal times!
Or as an alternative, change your sleeping pattern so that you're not getting up so late.