One common theme is the clash of different cultures. Since Inuyasha is set in a feudal Japanese - like world, when it crosses over with other universes, like a modern - day or a different fantasy world, there's always this interesting cultural exchange. For instance, when crossed with a Western - based fantasy world, the differences in magic systems, social hierarchies, and values become a major part of the story.
One common theme is the clash of different power systems. In Bleach, there are the Soul Reaper powers like zanpakuto and kido, while in Inuyasha there are demon powers and spiritual powers like the Tessaiga. Fanfics often explore how these powers interact when the two universes collide.
One great 'inuyasha crossover fanfic' is 'Inuyasha and the World of Harry Potter'. It combines the magic of the wizarding world with the feudal Japan setting of Inuyasha in a really interesting way. The characters interact in unexpected ways, like Inuyasha being confused by magic wands.
Another great one is 'Bleach - Inuyasha: Crossover of Powers'. It focuses on how the powers from both universes interact. For example, the zanpakuto powers from Bleach and the demon powers in Inuyasha are pitted against each other in some epic battles, and the characters from both series have to team up to face a common, powerful enemy.
One idea could be that Sephiroth somehow gets transported to the feudal era of Inuyasha. He might initially be seen as a great threat due to his power. But as the story progresses, he could form an unlikely alliance with Inuyasha and his group against a common enemy, like a powerful demon that is even more menacing than any they've faced before.
One idea could be that Sakura, with her medical ninjutsu skills, ends up in the Feudal era of Inuyasha. She could help treat the wounds of the villagers who are often attacked by demons. Inuyasha might be initially suspicious of her strange powers but gradually come to respect her as she proves her worth in battles and in healing the injured. For example, when Inuyasha gets seriously injured in a fight against a powerful demon, Sakura's medical skills could be the key to saving him, which would change his view of her.
Well, perhaps the Sacred Jewel from Inuyasha somehow gets linked to the Spirit World in Yu Yu Hakusho. Kagome and Inuyasha follow the strange energy trail to the Spirit World. There, they meet Yusuke and Kuwabara. They find out that a powerful spirit in the Yu Yu Hakusho world is corrupted by the dark energy of the Sacred Jewel fragments. So they all have to work together to purify the spirit and restore balance to both worlds. The differences in their fighting styles, like Inuyasha's swordsmanship and Yusuke's martial arts - based spirit attacks, would make for some cool battle scenes.
There's also 'The Millennium Puzzle in Feudal Japan'. In this fanfiction, the Millennium Puzzle ends up in the hands of Kagome. As she tries to figure out what it is, she accidentally activates it and Yami Yugi appears. Together, they must find a way to get Yugi back to his own time while also using Yami Yugi's powers and knowledge of the Shadow Games to defeat various demons that are causing chaos in the area.
Inuyasha would probably be very wary of Sephiroth at first. Inuyasha is used to dealing with demons and his own set of problems in his world. Sephiroth's otherworldly power and cold demeanor would make Inuyasha see him as a potential threat. He might even attack first out of instinct.
I think Kurama and Kagome would be an interesting pair. Kurama, with his calm and intelligent demeanor, and his ability to use plants and nature - based powers in combat, could learn a lot from Kagome's knowledge of spiritual powers and the Sacred Jewel. Kagome, on the other hand, could be intrigued by Kurama's complex past as a demon - turned - good. They could exchange ideas about how to deal with demons and use their respective powers more effectively. And their more gentle personalities compared to some of the other characters in their respective shows could lead to some really interesting character - development - focused interactions.