Akeno would also be an interesting character for Percy to interact with. She has a mysterious and alluring personality. Percy, who is used to dealing with the goddesses in his world, would find Akeno's charm and power both familiar and yet different. Their interactions could involve Akeno trying to tease Percy, while Percy tries to stay focused on his own goals in the DxD world, and this could lead to some really engaging and sometimes tense moments between them.
Issei would be really interesting. He's the main character in DxD and has his own set of powers and a rather unique personality. His pervy nature would contrast with Percy's more heroic and sometimes serious demeanor. Their interactions could be both comical and lead to some great character development for both.
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.
In some fanfictions, Hermes interacts with Percy as a mentor. He might offer advice on how to deal with other gods or mythical creatures. For example, he could tell Percy the weaknesses of a particular monster. In other stories, he may be more of an enigma, his actions and words being hard to decipher. Sometimes, Hermes and Percy form an alliance, like when they have to face a common threat together.
One possible plot could be Percy arriving in the DxD world and being mistaken for a new, extremely powerful devil. He then has to navigate the complex politics of the devils while also trying to find a way back home. Along the way, he uses his demigod powers in unique ways against the various threats in the DxD universe.
He would surely interact with Annabeth. Their relationship is central in the Percy Jackson series, so in a Tartarus fanfic, she'd likely be there to support him or be in a similar situation as him.
Well, Annabeth would definitely be one. She's always been by Percy's side, and in this fanfiction, she might be a bit worried about Percy being the champion of Nyx. She could be trying to help him while also being cautious of Nyx's motives.
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.
Draco Malfoy would be a likely character. Given his Slytherin status, he would likely have a complex relationship with Percy. He might start off as hostile, seeing Percy as an outsider, but then they could end up having to work together for some reason.
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.
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.
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.