Naruto could be a disruptor of the status quo. In the Highschool DxD world, there are set power structures and politics. Naruto, with his straightforward and often naive view of right and wrong, would likely not abide by some of the more underhanded practices. He'd probably be a force for good, using his ninja skills and Kurama - enhanced power to protect the weak.
One way could be that Naruto's skills and values from his own world clash and then blend with the supernatural elements in Highschool DxD. For example, his strong sense of justice might lead him to oppose some of the more chaotic or immoral actions in the DxD world. And his ninja techniques could be a new and interesting addition, like using shadow clones in battles against devils or fallen angels. Kurama could also play a role, perhaps his chakra influencing the power dynamics in the DxD setting.
He could be a sort of outsider who comes in and shakes up the status quo. Naruto's unique powers would make him a force to be reckoned with. He might initially be confused by the different rules and power systems in Highschool DxD but quickly adapt. For example, he could use his shadow clones to gather information about the different groups and their motives. And his positive attitude could inspire some of the characters in the Highschool DxD universe to change their ways.
She might be a mediator between different factions. Since she has experience dealing with different groups in the Naruto world, she could try to bring peace between the devils, angels, and other races in the DxD world. Also, her unique sense of justice could influence the characters in DxD to be more morally upright.
In this fanfiction, Shirou might be seen as an enigma. His calm and collected demeanor would be different from the more boisterous characters in Highschool DxD. He could potentially be a mediator between the different groups, given his own experiences with complex moral situations in the Fate series.
Ichigo could be a game - changer. His Hollow - like powers might be mistaken for some sort of demonic or otherworldly ability in the Highschool DxD setting. This could lead to both misunderstandings and interesting interactions with the characters there.
Naruto could be a game - changer. He'd likely become a powerful fighter. His rasengan and other jutsu would be very effective against the enemies in the DxD world. Maybe he'd be seen as a new type of supernatural being due to his chakra. He might also use his ninja stealth to gather information about the various factions, which could be crucial in preventing wars between them.
One idea could be that Naruto is somehow transported to the world of Highschool DxD. He could use his ninja skills and chakra in the new world, maybe even teach some of the characters there a thing or two about combat. For example, he could show Issei how to better control his power using chakra control techniques.
The storylines can be combined by creating a common threat. Suppose an enemy emerges that is interested in both the power of the Bijuu and the power sources in Highschool DxD. This would force the characters from both universes to team up. Also, the cultural differences between the Naruto world and the Highschool DxD world can be explored. Naruto could introduce concepts like ninja clans and shinobi training to the DxD characters, while they could introduce him to the complex social hierarchies and supernatural politics in their world.
Ulquiorra could also be a part of a secret organization in the Highschool DxD fanfiction. This organization is interested in his powers and wants to use them for their own ends. Ulquiorra has to decide whether to go along with their plans or break free and find his own path in this new world filled with strange beings and even stranger politics.
He could play the role of a mentor. Since he has godlike powers, he could teach the characters in Highschool DxD new ways of fighting or using their powers more effectively. For instance, he could show the devils how to better use their magic in a more stealthy and efficient way, just like how ninjas use their skills in Naruto.