Oh god, he sounds like my step-sister's kids. I don't know about your nephew but mine are complete a**holes because their parents don't want to 'stifle' them. When the oldest, Max, was 3-ish he asked for a sip of my soda, which I gave him, and then threw a FIT when I asked for it back. What finally made him give it back you ask? A brand new soda of his very own delivered into his grimy little mitts by his mother. Meanwhile I got the one with kid spit, argh.
More recently they visited (oldest is now 6 and enjoys activities such as flinging fishing rods about the house with no regard for people's eyeballs or breakables) and the younger one, Caleb, (2) repeatedly kicked my sister and laughed when told to knock it off already.
Their form of discipline go something like this,
Max continues negative behavior.
Max does NOT stop.
Max keeps going.
Max finishes doing whatever it was (opening something he wasn't supposed to, tearing something to pieces, whatever) and wanders happily away to the next act of destruction.
It makes family time a real pain in the neck and my poor step-mom has a hard time bonding with her grandkids because they just plain suck to be around.
By contrast, my best friend's kid, Julien, who is only a few months younger than Max is VERY well behaved. His parents have always been strict about polite behavior and following rules but aren't screamers or spankers, just firm believers in the power of time out. When visiting I hear things like, "When you don't listen to what I say it makes me feel very frustrated, I would like for you to take a time out." and "It makes me sad when you aren't nice to your things and throw them around. Please pick them up."
Julien's one failing is a flare for drama. He in known to, when heading to time out, tearfully shriek a variation of, "I am feeling very hurt that I am being punished!" I think it's cute but I don't live there, my friend says it drives her a little batty.
Anyway, now that I've vented, no it doesn't sound like entirely normal behavior (although sometimes four can be a rough age). Either his parents aren't disciplining him effectively, he has some kind of organically based behavior disorder or a combination or the two and he's a fine little sociopath in the making. I hope for your sake (and your daughter's) that this lovely branch of your family tree lives far enough away that you don't have to see them much.