Greed has to do with money. There was no money in Eden.
Covetousness has to do with desiring what you don't have. Adam/Eve had everything in Eden.
Envy/Jealously has to do with wanting what others have. Adam/Eve were content with what they had, possession-wise.
Their sin was pride - to be like gods.
Greed isn't only about money, it is about wanting to accuмulate more and more without reason. It is also possible to be greedy about knowledge, and wanting to accuмulate knowledge even things you shouldn't be privy to is the sin of curiositas, which is one of the sins Adam and Eve committed when they desired the fruit of knowledge.
For envy, well, I think Adam and Eve envied God's knowledge. And if they were content with what they had, (which is a virtue), they would not have sinned.
Pride is the root of all sins, but not all sins are pride. Because Adam and Eve had perfect control over their body's impulses, they couldn't be tempted the same way we are, but they had to deliberately pursue temptation which requires pride (putting one's desires above what God's will).