A common theme is the clash of different power systems. Naruto has his chakra and various jutsu, while Inuyasha has his demon powers. When the Juubi is added into the mix, it creates a complex power dynamic.
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.
Well, you can start by looking on fanfiction.net. There are often a good number of crossovers there. Just search for 'juubi naruto inuyasha crossover' in the search bar and you'll likely find some interesting reads.
In this kind of fanfiction, Naruto becoming the Juubi would completely change the Naruto universe. It would mean he has an insane amount of power. He could potentially reshape the world, bring peace in a way no one expected. His relationships with other characters like Sasuke would also be very different. Sasuke might be both in awe and a bit jealous of this new power Naruto has.
Naruto becoming the Juubi in a crossover fanfiction could lead to new alliances. Other characters from different series might see him as a valuable ally or a threat. For instance, characters from Bleach might approach Naruto differently. And Naruto himself might have to decide who he can trust with his new power.
Well, it could be about Naruto having to face a new and more powerful form of the Juubi. Maybe the Juubi has some new abilities or is being controlled by a new villain. Naruto would then have to gather his friends and allies, train harder, and discover new powers within himself to defeat this new threat.
One possible plot could be that the Juubi from Naruto somehow breaks through dimensions and ends up in the Bleach universe. This could cause chaos as the spiritual energy in the Bleach world reacts to the Juubi's massive chakra. Ichigo and Naruto might team up to stop the Juubi. Naruto could use his sage mode and Rasengan techniques, while Ichigo uses his Bankai. They would have to learn to combine their powers and fighting styles to defeat the Juubi and send it back to its own universe.
Well, one possibility could be that Naruto, with the power of the Juubi, enters the DxD world. He might use his ninja skills and the Juubi's immense power to face off against the devils and other supernatural beings in the DxD universe. Maybe he forms alliances with some of the characters there, like Issei and his friends, and together they fight a common enemy that threatens both the ninja world and the DxD world.
Well, if Naruto absorbs the Juubi in a crossover fanfiction, he would likely become extremely powerful. His already formidable chakra reserves and abilities would be enhanced to a whole new level. He might gain new jutsu or the ability to manipulate the world in ways he couldn't before. Maybe he could even use the power of the Juubi to achieve peace in the ninja world more easily.