"More tea, Vicar?"
Considered to be the very best of "literary nonsense" at the time of its publication, I'm fairly sure that each of the characters can be explained, eventually. I'm no psychiatrist but I'm sure that the characters will be a mix of incestuous brothers and sisters, cousins, aunts and uncles. It has all the hallmarks of being a real family dynamic, however preposterous the idea may seem by today's standards. You don't have to troll back too far through the annals of time to note that incestuous liaisons were quite common among the aristocracy.
That said, this argumentative, family dynamic, is all about power, of greed and money but, more disturbingly, is one driven by the person who has the most controlling influence over the other, less dominant, siblings. It is a simple case of "eat or be eaten!" They have their own reasons for being the person they choose to be. It's as if they seem to have some sort of synaptic mechanism hard wired in to their brain, one that tells them that if they are feeling sad, then it's only right that they make everyone else feel sad as if to even things out.
Perhaps now would also be a good time to point out that if each of the siblings were tested for a specific chemical element, one that matched their own persona, then we would be talking about a very highly explosive mix, something akin to that of nitroglycerin, a volatile mix that would need little persuading to make it combust.
The art of survival is knowing when things are about to BLOW and to remove yourself to a place of safety ahead of time.