The powers of Greek gods could be incorporated by having characters inherit some of those powers. For instance, a wizard might gain the ability to control the weather like Zeus. This would create a new type of magic in the Harry Potter universe.
In fanfiction, the Greek gods could bestow their powers on certain characters as a form of reward or punishment. If a Harry Potter character does a great service to a Greek god, they could be given the power of Hermes, like super - speed or the ability to travel between dimensions easily. This would not only introduce new powers but also new moral and ethical dilemmas for the characters as they deal with these new - found abilities.
Jean Grey's telepathy can be used to read the minds of wizards and witches. In the 'Harry Potter' universe, this could be a huge advantage. For instance, she could easily figure out the plans of Death Eaters or other dark wizards.
Kamui's powers could be incorporated as a new form of magic in the Harry Potter universe. For example, his ability to phase through objects could be seen as a very rare and advanced form of apparition that only a few, like him, can master.
Venom's ability to heal quickly could also play an important role. In the Harry Potter series, injuries are common during battles and duels. A character with Venom's healing factor would have an advantage. They could survive attacks that would normally be fatal and keep on fighting. This could change the dynamics of battles in the fanfiction world. For example, if Harry was bonded with Venom, he could survive Voldemort's Killing Curse due to Venom's healing ability.
Medusa can be incorporated as a dark magic - created being. Maybe some dark wizard in the past tried to create a powerful weapon and ended up with a Medusa - like entity. In fanfiction, this could be the start of a new adventure for Harry and his friends as they try to stop this entity from causing chaos in the wizarding world.
In fanfiction, a Pegasus could be a symbol of great power or prophecy. It could be foretold that only a chosen wizard can tame a particular Pegasus, and this wizard will then be able to use the Pegasus's power to defeat a great evil that threatens the wizarding world. This would create an exciting plotline full of mystery and adventure.
Kirin could be incorporated by being a guardian of a hidden magical artifact in the Harry Potter universe. This artifact could be something that has the power to change the balance of magic. Harry and his friends might stumble upon the Kirin while searching for the artifact, and they have to earn the Kirin's trust to gain access to the powerful item.
Greek gods can be incorporated by having them associated with the properties of lemons. For example, a god of fertility could be linked to the growth of lemon trees. Or a god of wisdom could use lemons in a riddle or a test for mortals.
It could be a magical item with a mind of its own. In fanfiction, the Blue Scarab might choose Harry as its owner and guide him through a series of challenges. It could have the ability to transform into different forms, like a key to open secret passages or a shield to protect Harry from dark spells. This would add an interesting dynamic to the story as Harry has to learn to communicate and work with this strange new entity.
The Crimson Dragon can be a protector of a hidden magical artifact in the Harry Potter fanfiction. For instance, it could guard the Philosopher's Stone in a more complex and dangerous way than Fluffy did in the original story.
Valyrian Steel could be part of an ancient prophecy in the Harry Potter fanfiction. Maybe it's said that only a wizard with a pure heart and a connection to the founders can wield a weapon made of Valyrian Steel. Harry, being the hero, is destined to find and use it to defeat the ultimate evil. It could also be that the Valyrian Steel is hidden in a different magical realm that Harry has to travel to, which would introduce new and exciting settings into the fanfiction.