At least in the Gemworld section. I'll be updating this as the book goes on.
The House of Amethyst:
Chandra: During the war of the Eclipse she found a way to Earth to take away a great evil and end the war.
Bhoj: Not in line for the throne because he can't tap into the family power. He has no loyalties and doesn't want to take sides since he thinks that would be a death sentence. Bhoj is 8 years older than Graciel.
Mordriel: Current ruler. Since she can't have her own child she wants her niece, Amaya, as her heir. More than willing to kill her sister, Graciel.
Graciel: Fleed to Earth to raise her daughter. Taught her how to fight but didn't tell her anything about her inheritance until they went back to their world on Amayas' 17th birthday.
Amaya: Heir to the throne, shares her power with her mother and aunt. She seems to have inherited a little of her fathers' powers too.
Amethyst Powers: Can form weapons, shields and projectiles in amethyst they create. They can also lift great weight.
The House of Citrine (A minor House):
Unnamed Grandmother of Ingvies': Who held the family power before Graciel left for Earth. When she felt her mind slipping away she transferred the power to her daughter, Senshe.
Senshe: Current ruler after her mother gave up her power. She wants her daughter to get the citrine power after her. Although she is loyal to Graciel she doesn't like change.
Ingvie: Amayas' friend who wants to stay an archer and doesn't want to inherit her familys' power.
Unnamed Brother of Ingvies': that she'd rather get the power.
Citrine Powers: So far what the family can do isn't clear but the stones can record messages and help people learn the native tongue.
The House of Diamond:
Reishan: Is in charge, apparently he killed his father to gain power. He was arranged to marry Graciel before she fell in love with another man, something that's sure to cause some bitterness. He was briefly married to Mordriel but it ended after two years. It's also been implied that he had more heirs than his current three at one point.
Zushan: The oldest heir that looks down on his own soldiers. Thinking he's entitled to anything because he's a prince. He's repeatedly threatened to kill Hadran since his brother was ten.
Hadran: Likes to hang out with their soldiers. His values bring him at odds with Zushan who's more than ready to kill him.
Talzanar: The youngest and most innocent son.
Diamond powers: Unknown.
House of Onyx (Minor House?):
Ella and Eiya: The house of Onyx seem to be a group that are hired to do odd jobs but take no sides. They are to follow ancient guidelines that restrict them from carrying out assassinations and such. Ella and Eiya dislike these rules and are hired by Mordriel to kill Graciel. Though they will be marked for death for taking such a job they agree when they are offered portal crystals. Amaya was forced to kill both of them to save her mother.
Lady Akikra: Helped Vyrian and Graciel by taking the portal crystal to hid for 17 years so Graciel and Amaya could return. She seemed moved by Vyrians' sacrifice and chose to avenge his betrayal.
Onyx Powers: Unknown.
House of Turquoise:
Firojha: Amayas' grandfather who gave up his power to offer protection only to regain it once his son died. He ended up betraying his own son to regain the power he lusted after. Even though his actions played no role in his sons' death (as Vyrian gave up his life for his family) he felt guilty for his actions and nearly spent all his House funds on a tome to honor his son. Lady Akikra, who helped Vyrian, killed him for his betrayal.
Vyrian: Amayas' father, who rediscovered the way to Earth and gave his life to power the portal crystal for his wife and daughter. At the time of his death was Lord of Turquoise.
Preet: A thief that turns out to be a "wild seed" of the House of Turquoise. Since Firojha has no official heir after he dies Preet inherits the powers.
Turquoise Powers: It seems to be implied that they can transform or create illusions. Amaya was able to reverse her fathers spell on her clothes to transform them into earth clothes.
Ruby Powers: I don't know if there's a House but the ruby stone heals.