In this kind of fanfiction, Harry often becomes more proficient in potions and other areas that Snape is good at. His relationship with Snape also makes him more empathetic towards Snape's past and the Slytherin house in general. He may not be as quick to judge people based on their house. Also, he might develop a more complex view of the wizarding world's politics, as Snape is deeply involved in some of the darker aspects of it.
It can lead to a completely different dynamic. Harry might have a new perspective on Snape and the magical world.
Harry in this fanfiction might be a lot more complex. His identity is no longer that of the Boy Who Lived in the traditional sense. He has to come to terms with the fact that his parents are two very different and controversial figures. He may become more of an outcast, even among his friends at Hogwarts. His sense of right and wrong could be more blurred, as he has the influence of Bellatrix's dark ways and Snape's own morally ambiguous actions. He might be constantly questioning his own nature and whether he is destined to follow a path of good or evil.
He might become more in tune with nature. Since the Phoenix is a symbol of rebirth and nature in the wizarding world, Harry could develop a stronger sense of environmental magic. For example, he could be able to communicate with other magical creatures more easily, not just the Phoenix.
Snape's character in Harry Potter fanfictions often changes in terms of his relationship with Harry. Sometimes he is written as being less bitter. He may be more understanding of Harry's situation, especially considering Harry has lost his parents. In certain fanfictions, Snape might even be the one to help Harry with his emotional turmoil over his parents' death. He can also become more collaborative, working with Harry instead of against him. This could be due to different interpretations of his true nature that were not fully explored in the original series. Fanfiction writers often take the hints of his good side from the books and expand on them, making him a more rounded and sympathetic character in relation to Harry.
His loyalty becomes more evident. In the original story, his loyalty to Dumbledore was somewhat hidden under his grumpy exterior. In this fanfiction, as Harry is learning to trust him, Snape's loyalty to the side of good and his care for Harry become more pronounced. He might take more risks to protect Harry and Hogwarts, and his actions are no longer so easily misinterpreted as malevolent.
In 'Harry Potter son of Loki' fanfiction, Harry changes significantly. His sense of identity is greatly shaken. He no longer just sees himself as a simple wizard. He now has this connection to Norse mythology. This makes him more curious about different forms of magic and otherworldly things. He may become more of an outcast as well, since his heritage is so different. But this also makes him stronger in some ways. He has to rely on himself more and develop his own unique set of skills and powers that come from both his Potter and Loki lineage.
Harry in this fanfiction is likely to be more ruthless. Voldemort's upbringing would make him less empathetic. He may value power above all else and be more willing to use dark magic to achieve his goals. His relationships would also be different. He wouldn't have the same close - knit group of friends as in the original story. Instead, he might be surrounded by Death Eaters or those who follow Voldemort's ideology.
In this fanfiction, Harry's change is quite significant. Firstly, his view of himself and his place in the world is completely altered. Instead of just being a wizard, he is now part of something much bigger. This new identity gives him a different kind of courage. He's not just fighting for the wizarding world against Voldemort, but also has a connection to Asgard. His relationships with his friends also change. They might see him in a new light, and he might have to deal with their different reactions. He could become more of a leader, using his new powers and status to inspire others. And his magic might even be influenced by his Asgardian heritage, making it more powerful or having different manifestations.
In some fanfictions, Snape might use his advanced knowledge of potions to create a special concoction to heal Harry. He could draw on his skills in Herbology as well to find rare ingredients for the potion.
Often, Harry's development is more complex. He has to deal with two different worlds, the muggle world where he was raised and the wizarding world he belongs to. This dual - world experience can make him more adaptable but also more conflicted. For example, he may love his muggle family in some ways but also feel a sense of betrayal when he realizes they've been trying to keep him from his true nature. His relationships with other characters, like Hermione and Ron, may also be different as he has this unique background.