Our daughter is 2 and takes a paci at night, and generally at night (there have been occasional out-all-day and too cranky to function in the car on the way home scenarios). I talked to her pediatrician about it at her 2 year checkup because I was getting pressure from friends/family to ditch it, but I saw that it was generally still a very soothing thing for her. Our pediatrician, reassured me that if she doesn't have it in her mouth all day long, and isn't using it as a comfort object in a not-what-it-is-designed-for way, then she is still getting soothed by it and will eventually outgrow the need for it.
If you make it a rule to let him have it in his bed only--that might help. We put a little basket next to our daughter's bed and she gets to pick her paci before bed, and in the morning before she gets dressed, she puts it back in the basket. It helps her associate it with bedtime only--although I have caught her sneaking it occasionally when she's in her room playing! I don't make a big deal about it though, I just remind her that it's for nighttime and she then puts it back.
It sounds like he's had a lot of transitions in his life. You might want to rethink the potty training for the time being until he seems to regulate his sleeping. My mother's only real advice to me about potty training was--don't do it until they're ready. My baby brother potty trained in about a week when he was 3, my other brother took 2.5 years to train because my mom started him at 2 because she thought since I had figured it out at 2, that must be the age. She learned that every child is different, and pushing/pressuring my brother just resulted in him being stubborn and wanting to control the situation even more.