How do i deal with this?

Maybe the best thing to do would be to sit down with him and express some of these feelings out loud. He may not have any idea that his behavior is leading to a situation where you feel hurt. He may even be staying busy on purpose because he doesn't want you to feel as if he needs to be constantly entertained. Or, maybe he's just a restless person who likes to always be out doing something. I don't know - but you must have some idea of why he does what he does, or what type of personality he has.

It's normal to be aware of the fact that your surviving family is smaller today than it was in the past. It would not be helpful to your family relationships to deny him from staying with you. Rather than worrying yourself over the situation to the point that you're making yourself sick, a simple discussion could help to clear things up, or at least give you a better idea of how to handle the relationship in the future.

EDIT: You say you have spoken to him about this before. So, maybe his way of dealing with similar feelings of loss and fear of losing family members is to just avoid talking about or dealing with his own feelings. He may be avoiding you, at times, because he hasn't yet figured out for himself how to handle his own feelings. In this case, maybe the best thing is not to try to press forward with any more talking. Try your best to enjoy what time you do have together. You love your brother, so give him some time and space to figure things out for himself - because he may not have dealt with his own fears and feelings yet, and he may not really even know how to.

Try taking him out like he does for you, or just plain confront him and tell him how you're feeling, that would be best :)

He's your nephew, not your boyfriend. Tell him you'e taking him somewhere or tell him to f*kc off. Whatever makes you feel better.