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.
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.
Power combination. Since both Naruto and Fairy Tail have their own power systems, a common theme is how the powers like Naruto's ninjutsu and Fairy Tail's magic can be combined when the two worlds collide. Another is friendship. Fairy Tail is big on friendship, and Naruto also values comradeship, so this is often explored when the characters from both universes interact in these crossovers. And of course, the threat of the Juubi is also a major theme as it forces the characters to work together.
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.
Power and growth. Both Inuyasha and Bleach have characters with different levels of power. In crossovers, often a character from one series has to adapt and grow in the other's world, facing new challenges that test their power.
One common theme is the clash of different worlds. Inuyasha is set in a feudal era full of demons and magic, while Ranma has a more modern (but still very Japanese - culture - influenced) world with martial arts and strange curses. So when the two are crossed over, the difference in their worlds often leads to interesting plotlines. Another theme is the interaction between the characters. For example, Inuyasha's brash and impulsive nature vs Ranma's own quick - tempered but also comical personality can create a lot of humorous and tense situations.
One common theme is friendship. Since both Naruto and Inuyasha value their friends highly, in fanfictions, they might bond over their shared experiences of protecting their loved ones. Another theme could be power - ups. Writers often like to give the characters new abilities or enhance their existing ones when they are in a crossover situation.
The theme of redemption can also be found. There may be characters who have made mistakes in either the Inuyasha or Naruto universe and in fanfiction, they get a chance to redeem themselves by helping in the fight against common foes. Additionally, the exploration of different powers is a big theme. How would the spiritual powers in Inuyasha work with the chakra - based powers in Naruto? Fanfictions often play around with this idea, creating unique power combinations and battles that are really exciting to read about.
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.