If Rowena Ravenclaw raised Harry, his magical abilities could develop in a more diverse way. Ravenclaw was known for her creativity, so Harry might be more experimental with his magic. He could combine different spells or create new incantations based on his understanding of magic principles. Also, he might have a better control over magic related to the mind, like Legilimency and Occlumency, as Ravenclaw would likely value mental discipline and knowledge of the self.
His magical abilities might develop with a greater emphasis on intellectual magic. Since Rowena Ravenclaw is associated with knowledge and wisdom, Harry could be more inclined towards spells that require deep understanding and study. For example, he might master complex transfiguration spells earlier because Ravenclaw would encourage him to study the theory behind them thoroughly.
His magical abilities might be influenced by the Norse magic system. He could have a more primal and elemental approach to magic, perhaps being able to control natural forces like thunder (associated with Thor) or ice (linked to some Norse entities).
Harry could develop a more unique style of magic. His grandfather might have his own way of doing magic, and Harry would learn from that. For example, his grandfather could be more in tune with nature magic, and Harry would then incorporate that into his spell - casting, making his magic more diverse and less reliant on the traditional Hogwarts curriculum.
Their relationship could start with mutual respect. Harry, being a curious and brave wizard, would be intrigued by Rowena's wisdom and knowledge. Rowena, seeing Harry's potential and his unique experiences, would take an interest in him. They might start by having conversations about magic, with Rowena sharing her ancient insights and Harry contributing his modern - day experiences. As time goes on, they could become something like mentor - mentee, with Rowena guiding Harry in areas of complex magic.
His character would likely be more confident. Growing up with a loving mother like Lily, he wouldn't have the insecurities that came from the Dursleys' treatment.
Since Vegeta has a very different upbringing compared to the Dursleys or the wizarding world in general, Harry's magic would be shaped by Saiyan values. He might be more inclined to use magic in ways that enhance his physical abilities, like using spells to increase his speed or strength during combat. This would make his magic development more about augmenting his body's natural capabilities rather than just learning traditional wizarding spells.
If Harry Potter was raised by Odin, his magic would take on a whole new dimension. Firstly, his connection to the magical world would be through a very different lens. Odin's knowledge and power are vast, and he would likely train Harry in a much more rigorous and perhaps less structured way than Hogwarts. Harry's magic could be more in tune with nature and the cosmos, as Odin has strong ties to such elements. His ability to communicate with magical creatures might also be different. He could have a more dominant and assertive approach, as Odin's leadership style is quite forceful. His magical skills might not be as refined in the traditional Hogwarts sense, but they would be more adaptable and powerful in a different context.
His magic might develop with a more physical aspect. Since Kushina was a ninja, she might encourage Harry to use his magic in more combat - related ways, like combining spells with physical movements, rather than just relying on the traditional wand - waving.
Since McGonagall has a strong sense of justice, Harry would probably have an even more acute sense of right and wrong. He would grow up with her values of fairness and loyalty deeply ingrained. This could lead to him being more proactive in standing up for others who are being wronged, not just because of his own experiences, but because of the values he was taught by McGonagall.
His magical abilities would likely develop at a much faster rate. The founders are extremely powerful and knowledgeable. They could guide Harry to discover and master magic that most wizards his age wouldn't even know exists.
His magical abilities would likely be developed in a more archaic and powerful way. The founders had different areas of expertise, so Harry could inherit a wide range of skills. Maybe he'd be a master of defensive magic like Salazar Slytherin was known for some aspects of it, and also be proficient in charms like Helga Hufflepuff was with her kind magic.