He'd likely be more attuned to the darker aspects of magic. Since the Hel Gods are associated with darker realms, Harry might not shy away from what's considered 'dark magic' as much as in the original story. He could be more of an outcast among the regular wizards who fear his different upbringing.
Perhaps in this fanfiction, the Hel Gods raise Harry to be a sort of mediator between the wizarding world and the underworld. So he has to deal with dark creatures in a different way than in the original story. He might have to make deals with them or understand their motives better. And his role in the fight against Voldemort could be completely different as he has this unique background.
In a 'Harry Potter raised by Hel' fanfiction, Harry could have a very different social structure around him. Hel might surround him with beings from Norse mythology. He would learn different forms of magic, like rune magic perhaps. His relationship with Dumbledore would be non - existent or very different. He might not even attend Hogwarts. Instead, he could be trained in a place that combines the elements of the Norse underworld and magic. His character would likely be more brooding and less inclined to trust the 'light' side of the wizarding world as he was not influenced by the positive Hogwarts environment.
In Norse mythology, Hel is a figure associated with the underworld. In this fanfiction, she could be a character who has some sort of connection to the wizarding world. Maybe she's a powerful witch from a different magical realm that Harry encounters and eventually marries.
He'd be more reserved. Hel's influence would make him less likely to trust easily. He wouldn't have the same sunny disposition as he might have had if raised by the Dursleys and then influenced by Hogwarts. He'd be more attuned to the darker aspects of magic and life in general.
In such a fanfiction, perhaps Harry would grow up with god - like powers. He might learn magic in a completely different way compared to the original story. For example, he could be taught by the gods to control elements at a very young age.
Well, perhaps in this fanfiction, the reason for Harry being married to Hel is a magical prophecy. Their marriage could be a key to solving some greater threat. For example, Hel might have powers that are crucial in defeating a new dark force. And as they get married, they have to learn about each other's worlds and cultures, which would be a great source of conflict and growth.
He would likely be more confident. Growing up with gods would give him a sense of self - assurance that he lacks in the original story. He might be less hesitant in using his powers.
Well, it could be that the Greek gods see Harry as a special being. They raise him on Mount Olympus. He would be taught by Athena in wisdom, so he'd be not only a powerful wizard but also extremely intelligent. His upbringing among the gods would give him a different perspective on good and evil. When he returns to the wizarding world, he'd use the values and powers he gained from the Greek gods to fight Voldemort. Maybe he'd use the gift of prophecy from Apollo to foresee Voldemort's moves.
In such a fanfiction, Harry Potter would likely be exposed to a whole different set of values and teachings. The Egyptian gods are known for their complex pantheon and their influence on Egyptian culture. Harry might grow up with a sense of grandeur and a connection to ancient magic that is far removed from the British wizarding world. He could be trained in different forms of magic, perhaps more focused on elemental control or hieroglyph - based spells. And his relationship with other characters would be very different. For example, he might see Dumbledore as a strange and foreign figure rather than a mentor.