Goku Black might become a sort of anti - hero. He has his own sense of justice (albeit a twisted one in his original story). In the High School DxD world, he could oppose some of the more corrupt elements of the different factions while also causing trouble for the main characters as they try to figure out his motives. For instance, he could see the way some devils treat humans in the DxD world and decide to take matters into his own hands, but not in a way that the main characters would necessarily approve of at first.
In a High School DxD fanfiction, Goku Black could be a mentor figure in a very unorthodox way. He has great combat knowledge and power. He could train some of the characters, like Issei, in new ways of fighting. But his methods would be very different from what they are used to. He might push them to their limits and beyond, not really caring about the consequences in the same way the DxD characters do. His goal might be to create strong opponents for himself or to shape the DxD world according to his own vision.
Well, he could be a powerful antagonist. His skills and power from the Dragon Ball universe would make him a formidable foe in the High School DxD world. He might be interested in the power of the devils and angels there and try to take it for himself.
His ki - based attacks would be a new and powerful addition. In High School DxD, most of the powers are related to magic, sacred gears, and demonic or angelic powers. Goku Black's ki blasts would be a completely different form of energy that could catch everyone off - guard.
His Saiyan transformation abilities would be a game - changer. For example, when he transforms into a Super Saiyan, his power level would skyrocket. In the High School DxD world, this could make him seem like an unstoppable force. His speed would also increase exponentially, allowing him to dodge attacks from the fastest characters in the DxD universe with ease. His powers are based on physical and energy training, which is different from the more innate powers of the DxD characters, so it would create an interesting contrast.
Goku Black could potentially enter the High School DxD world through a dimensional rift or some sort of magical accident. Once there, his Saiyan pride and his dark motives (from his own story) could lead to him either trying to take over the various factions in the DxD world or simply looking for a worthy opponent. He might interact with the main characters like Issei, perhaps seeing him as a target to prove his superiority or a potential ally in his own schemes.
Goku's powers in a High School DxD fanfiction would be a game - changer. His ki attacks could be on a level that could potentially destroy entire areas in the DxD universe. His martial arts skills are also top - notch. In a fight, he would use his speed and agility to dodge attacks and then counter with his powerful punches and kicks. His transformation abilities, like Super Saiyan, would be a shock to the characters in DxD. They might not have any means to counter such a huge boost in power.
The character could be a catalyst for change. The EMS gives them access to powerful abilities. In the High School DxD world, which is often about power struggles and hierarchies, their presence could disrupt the status quo. They might inspire other characters to strive for greater power or to question the existing power structures. For example, if they use their EMS to defeat a powerful devil who has been oppressing others, it could start a movement among the weaker characters to stand up for themselves.
One interesting story could be about Goku arriving at the High School DxD world and accidentally getting involved in a Rating Game. His super strength and unique abilities would completely change the dynamics of the game. Another could be where he befriends Issei and teaches him some of his martial arts moves, enhancing Issei's combat skills in a new way.
His role could be that of a protector. Given his nature of protecting his friends in the Naruto series, he would likely do the same in the High School DxD world. He could protect Fem Kyuubi from those who might want to take advantage of her power. Also, he could be a bridge between the different species in the school, using his understanding of different types of people from his own world.
Firebrand could be a student in the High School DxD setting who has a strange connection to the Naruto world. Maybe they have dreams or visions of the Naruto world and start to develop ninja - like abilities in the High School DxD world. This could lead to them being an outcast at first, but as they grow in power, they become a key figure in protecting the school from threats that are both from the High School DxD universe and potentially threats that have some connection to the Naruto world.
Alduin could play the role of an antagonist. He might be seeking to conquer the High School DxD world, using his powerful abilities. His dragon nature gives him an edge in combat and destruction, which could pose a major threat to the various factions in the story.