The plot could involve the Juubi's chakra influencing some of the demons in the Inuyasha world. Naruto arrives and has to figure out how to stop this chaos. He might teach Inuyasha some of his ninja skills, and Inuyasha in turn could show Naruto how to deal with the demons. They could also find that the Juubi has some ancient connection to a powerful artifact in the Inuyasha world, and they have to stop an evil force from using this connection for their own gain.
It could be a powerful ninja from Naruto's world who has been corrupted by the Juubi's power and somehow ended up in the Inuyasha world. He wants to use the power of the demons in the Inuyasha world to make himself even stronger and take over both worlds.
The crossover would likely involve a lot of cultural clashes too. Naruto comes from a world of ninjas and feudal - like structures, while the Justice League is from a more modern, superhero - dominated world. This could lead to some comical moments, like Naruto trying to figure out how to use a cell phone or the JL members being confused by Naruto's headband. But when it comes to the Juubi, they'd have to put aside their differences. The Juubi's power might be so great that it could potentially destroy both universes. So Naruto and the Justice League would need to combine their powers, with Naruto using his chakra - based attacks and the JL members using their superpowers like Superman's heat vision, Green Lantern's constructs, etc., to take on this ultimate threat.
The Juubi could be the main villain or a major threat that brings Naruto and the Justice League together. Its massive power would be a huge concern for both parties.
It could be a really exciting story. Imagine Naruto's ninja skills combined with the powers of the Juubi in the world of Percy Jackson. Naruto might use his Rasengan against some mythical monsters. And Percy could show Naruto the underwater world of the demigods. The two different mythologies and power systems would create a lot of interesting conflicts and friendships.
Definitely Hinata. Since she has feelings for Naruto in the original series, she could be a part of the harem. Sakura might also be there as she is an important female character. From the Juubi - related side, maybe a female form of one of the tailed beasts. Also, Tenten could be included as she is a strong female ninja. And perhaps a mysterious female character who has a special connection to the Juubi's power.
In a crossover fanfiction, the settings could merge. For example, Camp Half - Blood could be visited by Naruto. The demigods would be intrigued by his chakra abilities, which are so different from their own powers based on the Greek gods. Naruto could teach them some of his ninja skills in return for learning about their combat techniques. And perhaps the Juubi's presence could disrupt the natural balance of the Percy Jackson world, leading to new and unexpected adventures for both Naruto and the demigods.
In such a crossover fanfiction, the universes could blend through shared quests. For instance, a new evil force that is interested in both the power of the Juubi and the powers of the Greek gods. Naruto and Percy would be brought together to fight this common enemy. Along the way, Naruto would introduce things like chakra and ninja tools to Percy, while Percy would show Naruto things like the Camp Half - Blood and his sword Riptide. This way, their universes would gradually merge.
A cool plot might be that a mysterious figure uses the concept of a harem to manipulate Naruto in the context of the Juubi. The harem members could be from different villages and have different abilities related to the Juubi's energy. Naruto has to figure out who is behind this manipulation while also dealing with his growing feelings for the members of the harem. He could discover that there is a deeper connection between the Juubi and the creation of this harem situation, and that by solving this mystery, he can prevent a greater disaster.
The plot could start with a strange rift opening between the Naruto universe and the Percy Jackson universe. Naruto, with the Juubi's power inside him, gets sucked into the Percy Jackson world. At first, there's a lot of confusion. The demigods are on guard, thinking Naruto is a new kind of threat. But as they start to communicate, they realize they have a common enemy in the form of a powerful being that wants to take advantage of the chaos caused by the rift. So, they team up to fight this enemy.