I'm not even close to being an expert in child behavior disorders, but I'm taken some psychology courses and dealt with a number of cousins and relations with behavioral issues over the course of my life. Here's my take on the situation:
Some children develop the emotional and congnitive skills to handle being told "no" more slowly than others. If you think about it, being denied a desire or whim is actually a fairly stressful event for a child; they simply do not have the reasoning capability to differentiate between a "want" and a "need" until they reach a certain stage of development, and can be prone to behaving as though being refused a toy is the same as being deprived of food. Denial can feel like a threat in such a case.
It may be that his ability to process stressful emotional situations hasn't matured to the stage where he comprehends that behaving this way when denied something he wants is unacceptable. This may or may not be exacerbated by the fact that he isn't receiving the "you can't have everything you want, when you want it" message at home, if that is indeed the case.
Socialization is important; this is why head start and preschool programs are so vital. Children then get used to answering to authority that doesn't come from their parents or at-home caretakers. I started school at a time when such programs were not required (I began kindergarten over a month before I was 5) and I had many more behavioral difficulties than my brother, who spent a year in head-start and a year in pre-k before beginning kindergarten. In my case, they nearly ended up holding me back a year in the second grade, not because I couldn't handle the school work (I had NO problems there), but to allow me time to develop socially and emotionally. If your nephew did not have a lot of exposure to other children and other authority figures before beginning school, that may be a large part of the problem.
It's not necessarily ADHD, though certainly that should be checked out. As someone who discovered she has ADHD at nearly the age of 30, I'm not one to downplay the significance of this possibility. Finding out I had it literally made my entire life from childhood to adulthood make sense in a way it never had before. I do think, however, that the ADHD diagnosis is sometimes used to try to cure children of, well, being children. Don't take him to just *anyone* for such an evaluation; make sure it's someone who specializes in ADHD and/or child behavioral disorders. Make sure whomever you see is outside the school sytem rather than the school counselor or nurse or whoever--people in those positions are frequently more concerned with making the teachers' jobs easier by tranquilizing the kids than in actually getting to the bottom of the problem.
Lastly, and this is pure speculation, one thing stood out at me about your description, and that is that you said your nephew does not have a father figure, but behaves fine when he is with you. I am going to assume that you are male (perhaps I am wrong in this) because you said you are the closest thing he has to a father figure. You also said you do not cater to his every whim.
Now, if he is used to authority coming from males (you) but not from females (his mother and grandmother) and if his teacher is female, that could be another cause of the problem. He has simply not learned to expect authority from females, which would explain why he is fine with you and not with his teacher. If that's the case, then two things really need to happen:
1) his grandmother and mother need to toughen up (this is the most crucial point, and probably, unfortunately, the least likely to occur)
2) he would benefit from a seeing a social worker, preferably male, who can help correct some of these behavioral patterns and teach him to respond to authority from females.
A male teacher might also help the situation, but that might not be an option, and it's certainly not an optimal solution--at some point, he needs to learn respect for female authority, so just shifting him to a class with a male teacher will only delay solving the actual problem.