Naruto as the son of Hermes would have some really cool powers. For one, he'd probably inherit the power of flight, or at least be able to jump really high and far like Hermes' winged shoes. His Rasengan could be modified to have a touch of Hermes' magic, perhaps making it more unpredictable or able to track targets better. He could also use his chakra to create illusions that are more powerful and realistic, like the tricks Hermes might play on his enemies. And his ability to befriend and lead others would be enhanced, as Hermes was also a bit of a leader among the gods.
His powers would likely include super speed, which is a common trait among Hermes' children. He could also have the ability to communicate with animals, as Hermes was also associated with that. And of course, he'd still have his ninja skills like his powerful kicks and punches.
Naruto, as the son of Hades, would have some really cool powers. His Rasengan could potentially be infused with the power of the Underworld, making it a much more deadly attack. He could also have the power of persuasion over the dead, which means he could make them tell him secrets or do his bidding. His ability to sense chakra in the Naruto world could be translated into sensing the life force or the 'essence' of beings in the Percy Jackson world. This would give him an edge in detecting enemies, whether they are living or undead.
If Percy was the son of Gaia and Tartarus in fanfiction, his power set would be a fascinating blend. From Gaia, he could potentially have the power of terraforming, reshaping the earth on a large scale. He might also be able to communicate with all forms of earth - bound life. From Tartarus, he could gain the ability to traverse the darkest depths of the underworld with ease, and perhaps even draw power from the primordial chaos there. This would make him a very different and much more complex character compared to his original form in the official series.
He could be a bridge between the ninja world and the demigod world. His skills and values from the Naruto universe could be introduced to the demigods. For example, his way of training hard could inspire them. And in battles, he might use his Naruto - style combat along with Zeus - given powers to protect his new friends and the demigod realm.
He would likely have a combination of chakra powers and the Force. His ninjutsu could be enhanced by the Force, allowing him to perform feats like telekinesis while using his regular jutsu. For example, when he throws a shuriken, he could use the Force to guide it with extreme precision.
He might have a combination of his ninja powers and some sort of fire - based quirk from Endeavor. His Rasengan could be enhanced with fire, creating a really powerful and destructive attack.
Well, one way it could work is by having Naruto possess the speed and cunning associated with Hermes. Maybe he could use his ninja skills in the world of Percy Jackson. For example, his shadow clone jutsu could be a really unique ability there. He could send clones to gather information quickly, just like Hermes' messengers.
He would likely have a combination of his existing ninja powers and Asgardian powers. So, he could still use his shadow clones, but also be able to summon lightning like Thor. Maybe he could even use his chakra to enhance his Asgardian abilities further.
Naruto's ability to transform, like his Nine - Tails form, could provide a physical advantage in combat. Percy could use his water powers to cool down Naruto if the transformation makes him overheat or to create a protective shield around him. The Son of Artemis might be able to use his tracking skills, which are enhanced by his divine heritage, to find enemies that Naruto and Percy might not be able to sense. His arrows could also be used to disrupt the chakra flow of enemies, while Percy's water attacks could short - circuit any electrical - based ninjutsu, and Naruto's ninjutsu could provide distractions for Percy and the Son of Artemis to attack.
Well, his powers might include not only water - based ones. Since he's a god, he could have some sort of divine influence over weather related to the sea, like creating massive storms or calming them at will. He might also gain the power to transform into different sea - related forms, such as a giant sea monster or a merman - like being. And his healing ability, which was already there because of his connection to water, could become so strong that he could revive the dead if they had a connection to the sea in some way.
In a fanfiction where Percy is the son of Hades and Poseidon, his powers would be truly extraordinary. He could have the ability to create portals in water that lead to the Underworld. This would give him an advantage in both battle and travel. His hydrokinesis could be tainted with the essence of death, so when he attacks with water, it could cause a draining effect on his opponents, sapping their life force. Additionally, he might be able to sense the presence of the dead in any water source, which could be used for both reconnaissance and protection.