One common theme is the clash of different cultures. Naruto's world is more about ninja villages and modern - ish (for a fantasy world) structures, while Inuyasha's is a feudal era world. So when they cross over, there's often exploration of how these different cultures interact.
Sesshomaru could also be a very powerful character in this crossover. He has his own powerful sword, Bakusaiga, and his inhuman strength and speed. He is very experienced in combat against demons. Compared to Naruto's friends like Sakura, Sesshomaru would likely be much more powerful in terms of raw strength and combat ability. But Sakura has her own medical ninjutsu and superhuman strength when she releases her inner power, which could also be useful in different situations.
One possible plot could be that a character from Naruto with the Rinnegan somehow gets transported to the Inuyasha universe. Maybe they team up with Inuyasha and his friends to fight a common enemy. For example, the power of the Rinnegan could be used to counter some of the powerful demons in the Inuyasha world. The character might also introduce new jutsu or abilities to the Inuyasha gang, which could change the way they fight battles.
Inuyasha's demon blood could interact with Naruto's Nine - Tails chakra. Since both are sources of great power, they might be able to create a unique power - up. Inuyasha could use the Nine - Tails' chakra to boost his speed and strength even further, while Naruto could learn from Inuyasha how to better control his inner 'demon' side. Their combined power could be used to break through powerful barriers or defeat extremely strong foes.
Well, one possibility is that Naruto's godlike powers could completely overshadow Inuyasha at first. But then, Inuyasha's unique demon abilities and his sword, Tessaiga, might start to make a difference. Maybe Naruto would be intrigued by Inuyasha's half - demon nature and they'd end up teaming up to fight a common enemy like a powerful demon or a rogue ninja.
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.
Well, in a Godlike Naruto crossover in Inuyasha fanfiction, Naruto would likely have a huge impact. His ability to make friends easily could lead to some interesting alliances. He might team up with Inuyasha and the gang. His chakra control could also help in dealing with the spiritual aspects of the Inuyasha world. For example, he could use his chakra to sense and counteract some of the more powerful demonic auras. And his sage mode could give him an edge in battles against the toughest demons in the Inuyasha realm.
A plotline could involve Naruto's Kitsune heritage being related to some ancient mystery in the Inuyasha world. For example, there could be a prophecy about a Kitsune from another world coming to save the Inuyasha world from a dark force. Naruto then has to discover his true role in this prophecy, all while dealing with the mistrust and different personalities of Inuyasha, Kagome, and the others. There could also be some romantic sub - plots, like Naruto developing feelings for one of the female characters in the Inuyasha world or vice versa.
One interesting plot could be that Naruto and his friends are on a mission and accidentally end up in Inuyasha's feudal Japan through some sort of magic portal. There, they meet Inuyasha and his group. Naruto's ninja skills could be put to the test against the demons Inuyasha usually battles. And perhaps they team up to defeat a powerful common enemy, like a super - strong demon that neither group could handle alone.
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.