In a fanfiction, Matilda could get lost in the wizarding world and Harry could be the one to find her. He would initially be confused by her Muggle - like appearance but then realize she has something special. Matilda, on the other hand, would be in awe of all the magic around her. They would bond over their mutual sense of justice. Harry would be impressed by Matilda's fearless attitude towards authority figures, which she developed from dealing with her horrible headmistress, and Matilda would be inspired by Harry's courage in the face of great danger.
Matilda could be invited to Hogwarts as a special guest lecturer by Dumbledore, who has heard of her extraordinary abilities. Harry would be assigned to show her around the castle. As they walk through the corridors, they start discussing the similarities and differences between the magic in Hogwarts and Matilda's own powers. They might also compare the challenges they've faced in their respective worlds, like Harry against Voldemort and Matilda against her cruel parents and the headmistress of her school.
They could interact through a magical portal that connects their two worlds. For instance, Supergirl could be curious about the magic in Harry's world and visit Hogwarts. She might use her superpowers to help in a Quidditch match, like flying really fast to catch the Golden Snitch before any of the players. Harry, on the other hand, could visit Metropolis with Supergirl and be amazed by the tall buildings and advanced technology.
One way for them to interact is if a wizard from the Harry Potter world has a special interest in the magic of Mowgli's jungle. This wizard could send Harry on an expedition there. When Harry arrives, Mowgli sees him as a strange intruder at first. But as Harry shows his good intentions, they start to work together. Mowgli could introduce Harry to the different parts of the jungle, and Harry could share stories of his adventures at Hogwarts. As they spend more time together, they realize that they can help each other. For instance, Mowgli's animal friends could help Harry find a rare magical plant in the jungle, and Harry could use magic to protect the jungle from a group of poachers who are after some of the magical animals.
In a fanfiction, Puck could be a sort of guide for Harry in the Forbidden Forest. Harry is often in danger there, and Puck, with his knowledge of nature and magic, could help him navigate through the forest and avoid dangerous creatures. Also, Puck might introduce Harry to some magical creatures that are unique to his world.
They could interact as classmates at Hogwarts. McGee might be in the same year as Harry and they study together, help each other with homework, and get into adventures in the castle.
They could interact through a magical portal. For example, Mulan could be curious about the strange new world she enters through the portal and Harry could help her understand the wizarding world. He could introduce her to things like wands and spells.
Another way is through a friendly rivalry. Artemis, with his brilliant mind, could compete with Hermione or other intelligent characters in the Harry Potter world in areas like spell - making or magical theory. They could learn from each other's different ways of thinking, with Artemis bringing in scientific thinking and the Hogwarts students sharing their magical knowledge.
She can be portrayed as a brave character. In some fanfictions, Matilda might be the first to volunteer for a dangerous task, like facing a dark wizard. This shows her courage and her willingness to protect the wizarding world.
They could interact through a cross - dimensional portal. Tony, being curious about the magic he detects, steps through the portal into the wizarding world. Harry is initially suspicious but soon realizes Tony's good intentions. They then start working together, with Tony using his gadgets to help Harry in his fight against dark wizards.
In this type of fanfiction, the interaction could be based on mutual interests. Maybe some Goa'uld are interested in the Philosopher's Stone for its potential to grant immortality. So they might try to make deals with the wizards. However, the wizards would be very cautious as they know the Goa'uld's reputation for being manipulative. This would lead to a lot of tense negotiations and possible betrayals.
They could interact through a magical accident. For example, a spell gone wrong could open a portal that brings Eyeless Jack into the Harry Potter realm. Harry and his friends might initially be scared of Eyeless Jack, but then realize he's not entirely evil. They could start to communicate and share knowledge, like Eyeless Jack teaching them about his own world's form of 'darkness' while they teach him about magic spells.