Well, in many fanfictions, their interaction begins with confusion. Since they are from different fictional universes, they have different ways of doing things. However, they quickly realize that they can learn from each other. Percy is impressed by Hermione's vast knowledge of magic theory, while Hermione is in awe of Percy's connection to the gods. They team up to face challenges. In some stories, they have to fight against common enemies that threaten both their worlds. During these battles, their interactions are intense. Percy might save Hermione from a monster, and in return, Hermione would use her magic to heal Percy's wounds. Their relationship grows stronger as they rely on each other more and more.
In fanfiction, the interaction between Percy and Hermione can be really diverse. At first, they might clash because of their different personalities. Percy is more laid - back and action - oriented, while Hermione is studious and rule - following. But as they get to know each other, they find common ground. For instance, they both have a strong sense of loyalty to their friends. They start to exchange knowledge. Percy shares stories about his quests and the Greek gods, which fascinates Hermione. Hermione, in turn, tells Percy about the magical creatures in the 'Harry Potter' world. Their friendship deepens as they explore each other's worlds together, and sometimes, this friendship can even turn into something more romantic depending on the fanfiction.
In these fanfictions, the demigods often try to understand the SCPs from their own perspective of good and evil. They might see some SCPs as new kinds of monsters to defeat. On the other hand, some SCPs could be seen as potential allies if they share a common goal. For instance, if there is an SCP that is being hunted by a more dangerous entity, the demigods could form a temporary alliance with it. The interactions are full of tension and discovery as the two different worlds collide.
The Avengers might be protective of baby Percy. They could use their skills to keep him safe from any danger. For example, Captain America could use his combat skills and leadership to organize the protection of Percy.
In some fanfictions, their interactions are filled with a bit of tension. Calypso, having been alone for so long, may be hesitant to fully trust Percy at first. But as he continues to visit her and bring her lemons, she slowly warms up. They start to share stories, with Percy telling her about his adventures at Camp Half - Blood and Calypso sharing her knowledge of the island's secrets. Their relationship builds over time, and the lemons can be seen as a symbol of their growing bond.
In some fanfictions, their powers might combine in unexpected ways. Maybe when Arya is in a tight spot, Percy's power somehow enhances her speed or strength. Or when Percy is having trouble controlling a large body of water, Arya's mental focus and determination help him gain better control. Their powers interacting can open up a whole new realm of possibilities for exciting and unique storylines.
The characters could interact in various ways. Percy could use his ability to understand Ancient Greek to communicate with the cavemen if they have some sort of connection to the old language. For example, if they are descendants of an ancient Greek - influenced civilization. Or, Percy might use his powers to perform feats that the cavemen would see as magic, and they would either revere or fear him based on that.
Annabeth, if she were with Percy, would be more interested in the architecture and strategic planning of Troy. She could offer her knowledge to the Trojans or the Greeks, but they might not trust her either. And Percy would have to protect her from those who might see her as a threat or a sorceress.
Percy would probably be very cautious around Morathi at first. Given his experiences with tricky and powerful beings, he'd be on guard. Morathi, being the conniving character she is, might try to charm Percy or manipulate him. For example, she could use her allure to make Percy lower his defenses, but Percy's loyalty to his friends and his own sense of right and wrong would likely make him resist.
Well, often their interactions start with hostility. Lucius, being a former Death Eater, would view Hermione as a threat to his pure - blood ideology. Hermione, on the other hand, would see Lucius as a symbol of the old, discriminatory ways of the wizarding world. But in some fanfictions, as the story progresses, this hostility can turn into begrudging respect. For instance, if they are both caught in a dangerous situation where they have to rely on each other's skills.
The settings are quite different. Percy Jackson often has settings like Camp Half - Blood, which is a place full of demigods training and living. In Highschool DxD, it's mainly set in a high school with a lot of supernatural beings. In fanfiction, they could interact in a way that the Highschool DxD characters visit Camp Half - Blood. They would be introduced to the Greek demigod way of life, and it could lead to some really interesting cultural clashes and exchanges of power.
Percy would probably be initially cautious when interacting with Egyptian gods. For example, when meeting Ra, the sun god, Percy might be in awe but also a bit hesitant as their powers are so different. He would need to show respect as he does with the Greek gods. The Egyptian gods, in turn, might be curious about Percy's abilities, especially his control over water which is not as prominent in Egyptian mythology.