Well, it could be that Harry summons Cthulhu accidentally. He might be experimenting with some new form of magic that he doesn't fully understand. Cthulhu's arrival would likely terrify everyone. The teachers at Hogwarts would have to figure out how to deal with this Lovecraftian entity. Some students might be drawn to Cthulhu's power, creating a rift within the school. And the Ministry of Magic would surely get involved, trying to contain the situation before it spreads beyond the wizarding world.
The plot might involve Harry using his magic in an unorthodox way to summon Cthulhu. Maybe he stumbles upon an ancient spell in the restricted section of the library. Once summoned, Cthulhu could bring chaos to the wizarding world. The dark and eldritch powers of Cthulhu would be in stark contrast to the more traditional magic in Harry Potter. This could lead to a struggle between the forces of Hogwarts and the indescribable horror of Cthulhu.
In a Harry Potter summons Cthulhu fanfiction, the plot could start with Harry having a strange dream or vision about an ancient and powerful being. His curiosity gets the better of him, and he decides to try and summon it. Cthulhu appears, and it's a being far beyond anything the wizards have ever faced. Its very presence could start to corrupt the magic around Hogwarts. The magical creatures in the Forbidden Forest might go into a frenzy. Harry would then have to decide whether he made a huge mistake or if there's a way to use Cthulhu's power for good, if that's even possible. All the while, he has to deal with the reactions of his friends and the wizarding community at large.
Hermione would be horrified. She's always by the book, and summoning Cthulhu is the most dangerous and unthinkable thing. She'd immediately start researching ways to send it back. Ron would be scared out of his wits but also a bit in awe of the power. Harry would be conflicted, realizing he's brought something extremely dangerous into their world.
The plot could involve Harry Potter being reborn in the Vampire Diaries universe with his magical abilities intact. He might face new challenges like dealing with vampires and witches in this different magical setting. Maybe he'd use his spells to protect himself from vampire attacks or form alliances with some of the characters. For example, he could team up with Bonnie Bennett, sharing magical knowledge. And he'd surely have to adapt to the different social structures and power dynamics in Mystic Falls.
There could be major power shifts. For example, the main characters might start to rule Hogwarts in an 'Overlord' - like way instead of following the traditional school hierarchy. Maybe Harry Potter himself could become more of a tyrant - like figure, using his powers not just for good but also for self - gain.
It could entail a story about a Nundu being used in the Triwizard Tournament as an unexpected and extremely dangerous challenge. The champions would have to figure out a way to survive the encounter with the Nundu without using dark magic.
In 'harry potter is a demigod fanfiction', we could see a lot of changes to the existing story. For example, the magical world might have to interact with the world of the gods. There could be new enemies, like monsters from Greek or Roman mythology. Also, Harry's relationships with his friends and teachers might be different. His identity as a demigod could make him both more powerful and more of a target. He might have to go on quests like a typical demigod, which would be very different from his normal Hogwarts adventures.
One possibility is that Naruto's connection with the summons would make him more in tune with nature. For example, if he was raised by toads, he might learn their unique jutsu faster and have a different approach to combat. He could also have a different view on friendship and loyalty as summons often have a strong bond with their summoners.
One possible plot could be that Harry discovers an ancient spell or artifact that allows him to summon angels during a time of great crisis in the wizarding world, like when Voldemort is at his most powerful. The angels could then offer their celestial magic to help Harry and his friends defeat the dark forces.
One idea is that there's a new spell in the Harry Potter universe that involves lemons and unicorns. Harry Potter could be the first to discover it while interacting with a unicorn. Maybe it's a spell that can transform things into lemon - flavored magical treats for a short time, and the unicorn is the key to unlocking this spell.
It would be really wild. Maybe Harry Potter would have some of Ulquiorra's powers like his cero blast, but in the form of a wizard spell. Or perhaps he would have Ulquiorra's cold and emotionless demeanor in the wizarding world, which would be a huge contrast to his normal self. He could be dressed in a way that combines the Hogwarts robes with Ulquiorra's Arrancar outfit.
It would probably involve Harry Potter having Spartan - like abilities. Maybe he could be super strong and agile like a Spartan, while still being able to use magic. It could also include elements of the Halo universe, like the Covenant or the UNSC, interacting with the wizarding world.