Is pregnancy possible while having the IUD mirena (levonorgestrel)? I have irregular period, so it's hard to know since I have been nauseous and eating more.

Take a test. It sounds like you're not sure, as in haven't been tested. It's more likely that something else is going on. Take a urine pregnancy test. If its negative and you're unconvinced, repeat in 2 weeks. If other symptoms appear: abdominal pain, vomiting, you need to see a doctor.
See your gyn. Do a blood preg test and an ultrasound, because if u have an iud and are preg , an ectopic is more common than if u did not have an iud and if u are pg , it can end up in the uterus, u sxs could be as u know from other causes.