Well, what are Hufflepuff’s values? Justice, loyalty and patience. Andrew has all three of them.
I think Andrew’s most prominent characteristic is his loyalty. Loyalty to his brother, that led him to kill their mother to protect him. Loyalty to his cousin, when he almost up those guys that hurt Nicky. Loyalty to his family, to Kevin, to Wymack and eventually to Neil. Every thing Andrew does, from when he stopped Neil from running away from Wymack to when he broken Riko’s arm after the last game, he does out of loyalty (on the first case, loyalty to Kevin and on the second to Neil.) Once Andrew decides to keep something or someone, there’s nothing he won’t do to protect it. You could argue that that’s a Gryffindor thing to do, but Gryffindors protect because they’re brave. Andrew protects because he’s loyal.
Andrew also holds justice as something really important. It’s his own sense of justice, of course, but after what he’s been through I don’t blame him for not have a “classic” idea of what is fair. Either way, it’s that sense of justice that guides his actions. He swore to protect his brother, so killing their abusive mother is fair. Neil is obviously a suspicious person, so it’s the right thing to push him to his limits until he finds the truth. Renee killed some people? They obviously deserved it, it’s fair. So yeah, Andrew Minyard lives first to be loyal, second to be just.
And finally, patience. I think Andrew is really patient. It takes a very extreme situations to make him act without thinking (like Neil getting kidnapped, which led him to choke Kevin) and, while that’s a bit Slytherin of him, I’m pretty sure Andrew isn’t ambitious enough to be classified as such. His patience is an acquired trait – he needs it to survive – and he only tosses it aside when the people he’s loyal to are involved.
Also I think it’s hysterical to imagine the following:
Professor: Aw, look at that tiny blond Hufflepuff going! Whatcha got there?
Andrew: A knife
Professor: NO!