They're twisted amalgams of human flesh and divine ichor, put together by genetics and something that doesn't show up under a microscope, but exists. The power of gods flows through them, deep as their bones, contained impossibly by human flesh. The process that put them together is so complex, so delicate, the the most minor addition of power (from, say, another deity hundreds of generations back) is enough to cause them to burn up and die from their own power.
They are freaks. Every single one of them.
—Ryuugi, describing the demigods.
Hazel's pretty bad, to be honest—she's very metallic, naturally, but the metals she brings up will doom anyone who touches them to horrible fates and and possibly deaths, and stuff like that shows under the Sight. The fact that she's dead and the fact that she lived a pretty crappy life don't do much to help, either.
But she's nothing compared to Nico and Percy, who are definitely the most horrific of the Greek demigods to look at—Thalia would rival them, but she shuns most of the expressions of her power, which really subtracts from her awfulness factor. It probably comes as no surprise that neither of them look human, though it may surprise some precisely how not-human they look. They're several hundred feet of not-human—titanic helpings of awfulness. Nico's a colossus of iron and dark stone and dead things, for example—and not silent or still dead things, either. Think rivers of forlorn, crying souls, flowing blood, and dead grasping hands, for instance, and the voice of the dead echoing his words in a chorus and worshiping him, etc.
As for Percy, he does have cephalopod traits. But primarily because is a monstrous amalgam of angry seas, buffeting winds, broken earth, and twisted oceanic biology. Even just sticking to seemingly organic stuff, he pretty much grabbed the buffet table of the sea. Tentacles, fins, gills, luminescent lures, scales, transparent portions, stingers, you name it. He's a little whaley, a little sharky, a little fishy, and more then a bit of everything else. He's got anemone of a few thousand colors and limbs that look like flukes or crab legs or tentacles or lobster claws or all of the above. His face is reminiscent of megalodons and angler fish and fangtooths and viperfish and black dragonfish and other stuff that is either extinct or down where people can't usually find them or both and should all stay that way plus a helping of nature's elemental fury, so his face, though it can make recognizable expressions, tends to default to either terrifying glee or titanic displeasure.
The only thing that keeps him from being completely disgusting or looking like someone sowed an aquarium together while everything (including the people) were still alive is the simple fact that a lot of the stuff in the ocean actually is quite beautiful and it somehow carries over under the Sight, so he ends up being fascinating and horrifying in pretty equal measure.
Honestly, that's what makes him to worst to look at, among the demigods—he's horrific and monstrous and yet hypnotic, in the way that a lot of marine creatures lure their prey to their doom. Nico's not as bad, relatively, because though he's horrific and mind-straining, he leans closer to the 'scream, shut your Sight, and run away territory' then to the 'stand there and weep with horrific joy while your brain melts' territory.
(There's also who he is as a person to help blunt the scream and run away factor, which is probably worse for anyone looking at him in the long run. It's like with, say...Angel or something, though on a much, much lesser scale—the fact that you want is not helping you in the slightest, because your brain is still sizzling like bacon.)
— Ryuugi, describing how Nico and Percy look under a wizard's Sight