The vampires' super strength and speed in Twilight could be a match for the physical abilities of some of the stronger demigods in Percy Jackson. For example, Emmett's brute strength might be on par with that of a son of Ares. However, the demigods have their own unique powers. Percy's control over water could be a huge advantage. He could create water barriers to keep the vampires at bay, as vampires are not that great with water.
The werewolves in Twilight have their own set of abilities, like enhanced speed and strength, and their ability to communicate telepathically. In a fanfiction where they meet Percy Jackson characters, their telepathic ability could potentially be used to communicate with some of the more intelligent demigods or creatures in the Percy Jackson universe. Meanwhile, the demigods' ability to fly (for some of them) or their healing abilities could be something that the Twilight characters would either envy or find very useful in a joint adventure.
Bella's shield - like ability in Twilight (her resistance to mental powers) could have an interesting interaction with the mind - controlling powers that some of the characters in Percy Jackson might possess. If there was a character in Percy Jackson who could influence minds, Bella would be immune to it. On the other hand, the demigods' ability to use magic items could be a mystery to the Twilight characters. The Cullens might be intrigued by the magical weapons and items that the demigods use in battle.
Well, Percy's ability to control water and Frozen characters' ice powers could create some cool interactions. For example, Percy could make a stream of water and Elsa could freeze it to create an ice bridge. It would be a great way for them to traverse difficult terrains.
If we consider the werewolves in Twilight, their strength and speed could be combined with Percy's strategic thinking. Percy, being a demigod, has been in many battles and could lead the werewolves in a more effective way against common enemies. For example, in a fight against a new supernatural threat, Percy could use his knowledge of different mythological creatures to come up with a battle plan, while the werewolves use their physical abilities to execute it.
Well, Percy's power over water is a very versatile thing. He can make water do all sorts of things like form into weapons or shields. Kratos, with his insane strength, can break through almost anything. In a fanfiction scenario, their powers could combine in battle. Let's say they're facing a horde of fire - based monsters. Percy could call up a huge wave of water to douse the flames, and then Kratos could rush in with his blades and start slashing away at the weakened foes. Also, Percy's ability to heal himself in water could be a great asset if Kratos gets injured. He could find a body of water and help Kratos recover, while Kratos could protect Percy during the process.
They might start with some mutual suspicion. Percy would be cautious around Thor as he's a very powerful being from a different mythology. Thor might see Percy as a bit of an oddity at first. But then they could start to exchange stories about their adventures. Percy could tell Thor about his battles with the Titans, and Thor could share his tales of fighting giants. This would lead to a newfound respect between them.
Annabeth, if she were with Percy, would be more interested in the architecture and strategic planning of Troy. She could offer her knowledge to the Trojans or the Greeks, but they might not trust her either. And Percy would have to protect her from those who might see her as a threat or a sorceress.
Percy would probably be very cautious around Morathi at first. Given his experiences with tricky and powerful beings, he'd be on guard. Morathi, being the conniving character she is, might try to charm Percy or manipulate him. For example, she could use her allure to make Percy lower his defenses, but Percy's loyalty to his friends and his own sense of right and wrong would likely make him resist.
They would probably start by being cautious of each other. Then they'd start to exchange skills and knowledge.
The demigods have a variety of powers. Annabeth's strategic mind could be combined with Alice's ability to see the future. They could plan out battles or ways to avoid danger. If a demigod like Jason with his lightning powers teams up with the vampires, they could use the lightning to create distractions or even as a weapon against common enemies. The vampires' super strength and speed could also be useful in getting the demigods out of tight spots quickly.
The Ghost Rider's hellfire ability would be a major factor. Vampires in Twilight are vulnerable to fire, so the hellfire could be a huge threat. Werewolves, on the other hand, are more in tune with nature. They might be able to sense the otherworldly nature of the Ghost Rider and either be in awe or try to fight it. The vampires' super - speed and strength might not be enough against the Ghost Rider's supernatural powers.
The two could have some really interesting conversations. Percy could talk about his adventures with Annabeth and the other demigods, while Jacob could share stories about his pack and his experiences in the forest. They might also compare their different kinds of powers. Percy's control over water and his ability to withstand a lot of physical damage compared to Jacob's enhanced senses and super - strength as a werewolf. And they could learn from each other. Percy could teach Jacob some Greek, and Jacob could show Percy how to track better in the wild.