He might have the power of foresight. Since he has lived for a thousand years, he could predict future events based on his past experiences. For instance, he could foresee an attack from an unknown enemy before it even happens.
He might have powers like shape - shifting into a more demonic form. Maybe he could have the ability to breathe fire or some other elemental powers related to chaos or destruction. He could also have enhanced strength and speed that are far beyond what a normal ninja has, and his senses could be super - sharp to detect danger or prey.
He might have the power of instant teleportation. Just like a god can appear anywhere, Naruto could do the same to surprise his enemies or reach his friends in need quickly.
He might have the power of Odin's All - Father magic. This could allow him to see the past, present, and future, just like Odin's ability to gain wisdom through his ravens. Also, he could potentially have enhanced physical strength, much greater than what he has as a regular ninja, allowing him to overpower even the toughest opponents with ease.
He would probably have powerful water - based abilities. For example, he could control the oceans and large bodies of water like Poseidon. He might be able to create huge tidal waves or even walk on water effortlessly.
He might have the power of charm. Just like Aphrodite can make people fall in love with a glance, Naruto could have a natural charisma that makes people trust him and want to follow him more easily. It could be really useful in his mission to bring peace to the ninja world.
He would likely still have his chakra powers. Maybe he could use chakra in ways that were similar to alchemy, like transforming matter. For example, he could use his chakra to change the shape of a rock into a weapon, much like how alchemists transmute materials.
He would have his Rinnegan as well. With the Rinnegan, he could potentially control the six paths of magic in the Fairy Tail universe. For instance, he could use the Deva Path to manipulate gravity - something not common in the Fairy Tail magic system. His Preta Path could absorb magical attacks, making him a formidable opponent against even the most powerful Fairy Tail mages. His other paths like the Asura Path could give him additional mechanical - like appendages with enhanced strength and weaponry, which would be a new and terrifying concept in the Fairy Tail world.
In this fanfiction scenario, Naruto would inherit a host of Saiyan powers on top of his ninja skills. For starters, he would have the Saiyan's natural fighting instincts and the ability to quickly recover from injuries. His power level would constantly increase as he fought, similar to how Saiyans get stronger through battles. His existing jutsus like the Rasenshuriken could be infused with Saiyan energy, making it not only cut through opponents but also blast them with a powerful ki - like force. And with his Saiyan tail, if he had one, he might have an additional form or power that was unique to him, perhaps something that combined the power of the Great Ape form with his Nine - Tailed Fox form.
If Naruto is revived by Edo Tensei, his powers could be quite interesting. His ability to heal would likely be different. Since Edo Tensei - revived bodies can regenerate, he might be able to recover from injuries even faster than before. In terms of combat, he could use his shadow clones more effectively. Maybe he can create a much larger number of clones without exhausting his chakra as quickly. Also, his perception skills could be enhanced. He might be able to sense danger or the presence of other ninjas from a greater distance. His overall power level would be a significant boost compared to when he was alive, and this would change the balance of power in the fanfiction's story.
He would have a whole range of powers. He could have the strength of Hercules to overpower his opponents. Also, the ability to control the wind like Aeolus from the Olympians. This would enhance his existing wind - style jutsu.