In fanfiction, it's possible to blend these worlds through a prophecy. There could be an ancient prophecy that foretells the coming of an Uchiha and an Uzumaki to the Harry Potter world at a time of great danger. The two characters, with their unique powers, team up with the Hogwarts students to fight against the dark forces. Their powers, like the Uchiha's genjutsu and the Uzumaki's sealing techniques, could be adapted to work in the wizarding world.
Well, you could start with a magical portal. A Uzumaki character, known for their strong chakra, accidentally opens a portal that leads to the Harry Potter world. An Uchiha, with their Sharingan, could be drawn to this portal as well, sensing the strange new magic. Once in the Harry Potter world, they could learn magic, and maybe even teach some of their ninja skills to the wizards.
The worlds can be blended by having Barbie visit Diagon Alley. She could be amazed by all the magical items and use her fashion sense to customize her wizarding robes. For instance, adding some sparkly elements that are typical of Barbie's style.
The blend can occur through the use of magic in relation to trigonometry in solving problems. For example, in a fanfiction, a magical creature is lost in a forest that is magically generated with trigonometric patterns. The characters need to use their knowledge of both magic and trigonometry to find the creature. Also, a character's magical power could be related to their understanding of trigonometry, so as they learn more math, their magic becomes stronger and more versatile.
A great way to blend the worlds is through a shared threat. A villain that uses both magic and technology to cause chaos. This would force Harry and Tony to work together. They would have to learn from each other's strengths and overcome their differences. Harry could teach Tony about the subtleties of magic, while Tony could show Harry how to use technology to gain an edge in battle.
In fanfiction, the characters could also meet during a special event. For instance, there could be a magical music festival that attracts both wizards and Muggles. Harry Potter and his friends are there for the magical elements, while Hannah Montana is performing. They cross paths and end up collaborating on a song that has magical properties, like making everyone who hears it feel extremely happy.
One way is through a portal. For example, a magical portal could open up between Hogwarts and Neverland. This allows characters from both worlds to interact. Harry Potter could enter Neverland and be shocked by the lack of traditional magic but also find unique magical elements there related to the island's magic. Captain Hook could enter Hogwarts and be amazed and also threatened by the powerful magic there.
Themes can be merged. The theme of good vs evil is present in both. In fanfiction, the dark wizards from Harry Potter could team up with the more malicious vampire clans in Rosario Vampire to create a super - evil force. And the heroes from both worlds would have to join forces to stop them. This would require characters to look past their initial differences and prejudices to fight for the greater good.
One way is through character crossovers. For example, a wizard could join the Sons of Anarchy as an undercover agent to protect the wizarding world from a threat that has ties to the biker gang. Or a member of the Sons of Anarchy could discover they have magical abilities and be sent to Hogwarts to learn how to control them.
One idea could be a crossover where a character with Uzumaki and Uchiha blood somehow ends up in the Harry Potter world. Maybe they have unique magical abilities that combine the Sharingan's powers with the Uzumaki's chakra control, and they attend Hogwarts. They could face off against dark wizards using their unique skills.
The worlds can be blended through character crossovers. For example, Vaan from Final Fantasy XIII could visit Hogwarts and be amazed by the magic there. He could try to learn magic spells, while also teaching the wizards about his world's combat skills.
The simplest way is through character crossovers. Have characters like Harry or Hermione meet and interact with Edward or Alphonse. They could exchange knowledge, with the Fma characters explaining alchemy and the Harry Potter characters sharing about magic spells. Another way is to blend the settings. For example, have Diagon Alley also include alchemical shops selling items like philosopher's stones or transmutation circles.