Here's a list of what Hades children can do in the books, I think we should agree on a certain limit to the amount that each power can be used, like if you pick one, the other can't be as strong
Geokinesis: He can control the earth - levitating rocks and making them deadly, black, and extremely sharp. Nico can open fissures in the earth that can swallow up creatures and trap them in the Underworld. He can cause earth tremors so powerful, they can shatter the pillars of a mountain fortress. He can also control the black walls of the Underworld. He has the greatest geokinetic ability of any demigod.
Necromancy: Nico can summon the dead, put the dead to sleep, and communicate with the dead. He also has divine authority and control over the Furies and the dead. He can banish the dead and release people who should have died (i.e. Daedalus). Some of his abilities in this domain includes the power to destroy Skeleton Warriors and physically manipulating ghosts, such as taking hold of them by hand or forcing them to be silent with a gesture. In The Last Olympian, he was able to summon a fairly large army of undead soldiers by himself. It is unknown how much he has increased in power since then.
Sensitivity to Death: He can sense death as it happens or when it is coming; when a person close to him dies, it comes as a ringing in the ears. He can also sense when an immortal is fading, as on the case of Pan. He can sense someone's life aura (he sensed it when Rachel Elizabeth Dare's life aura flickered, and he told her, "I could see you dying.") In addition to that, he has a deep knowledge of the Underworld and knows when a person's life is being judged in the Underworld.
Umbrakinesis: He has control over darkness and shadow for various uses such as solidifying it for attacks and to hide in it.
Shadow travel: He can use shadows as a way of transportation, however, great distances tend to wear him out. The first time he shadow traveled, he passed out for a week. He has said that while learning to use it, he ran into walls and made accidental trips to China.
Induced Fear: He radiates fear and death like his father, Hades, but to a much lesser degree.