He was fairly well off, no doubt about it. + His future was secured in every way thinkable. If he did this, I don´t think the primary reason was greed. To me the killings seem "personal", very violent and overkill, very messy (except in the case of Sheila); not the cool, calculated murders some guilters make them out to be.
Greed is part of the overall equation of it being personal.
He was mad he was forced to work instead of just being handed everything like he perceived was handed to Sheila and he considered her flat much better than the place he was given to live. He felt slighted by this any anything given to others that he felt should have been given to him. This is part of what made him fell angry towards them
Whether there was really overkill or not is hard to say. If he had killed his parents with a single shot each would he have bothered pouring so many into them? Would Nevill have been beaten if he had not needed to knock him out to be able to safely reload? The twins offer the only clue but how reliable is it? After his experiences with the parents one coudl see why he would want to pump several bullets ino them to make sure. He hadn't exactly proved to be capable of killing with 1 shot. For all we know they died last after he even failed to kill Sheila with 1 shot when he killed them. So pumping several rounds into their head could have been simply to make sure not from rage. It could also have been his effort to make it look like Sheila did it. Maybe he felt to make it look like she did it he needed ot make sure they had multiple rounds each.
Could it have been rage? Sure not only would his adrenaline have been pumping after the previous kills but he was very likely jealous of how much time Nevill was spending with them. Nevill was reportedly taking care of them all day. Jeremy was not happy at being dumped in a prep school and probably felt slighted by the attention they were being given. So he did have a reason of sorts that could have caused him to shoot them so many times.
It is just hard to know though if he was being motivated more by the planning of trying to frame his sister, being scared they would not die or emotions at that point. If it was these 3 combined how can you really pick which was the most significant? Would it even matter if one was more significant than the rest anyway?
If it was just a personal problem with the parents he probably would have acted earlier and against them only. The fact he waited until his his sister and nephews were there so they coudl be killed as well seems to demonstrate to me the main motivation was greed. Of course you have to have some emotional problems to be able to kill your parents for money so that certainly factored in.