In such a fanfiction, Naruto might experience extreme loneliness. He would watch his friends and loved ones die while he remains alive. He could also be hunted or studied because of his immortality, constantly on the run from those who want to use his unique condition for their own gains.
Madara Uchiha could also be an antagonist in this scenario. Even if he's dead in the original story, in the fanfiction, his influence or some sort of resurrection could occur. He might view Naruto's immortality as a hindrance to his own plans for the ninja world or simply be jealous of Naruto having such a power that he never had.
His character could develop in a very complex way. At first, he'd probably be confused and scared about the curse. But as time passes, he might use his immortality for good in a more extreme way. For example, he could take on the most dangerous missions without fear of death. However, the constant cycle of seeing people he loves die would also harden him. He might become more calculating and less impulsive, as he realizes the long - term consequences of his actions. He could also gain a deeper understanding of life and death, and maybe try to find a way to break the curse not just for himself, but for others who might be suffering from similar fates.
It could be due to a curse or a blessing. Maybe in the process of traveling between the Naruto universe and the DxD universe, some sort of magical energy latched onto Naruto and made him immortal. For example, it could be related to the Sacred Gears in the DxD world. A Sacred Gear could have malfunctioned or had an unexpected reaction when Naruto entered the world, granting him immortality.
Another plot could be that Naruto is given immortality as a reward for saving the ninja world. The Sage of Six Paths or some other powerful entity decides that Naruto's selfless deeds deserve such a gift. So, he bestows upon Naruto the power of immortality, which then changes Naruto's perspective on life and his role in the ninja world.
There could be a fanfiction where Naruto discovers immortality through a strange encounter with a mythical creature. For example, he meets a phoenix - like being that bestows upon him the gift of eternal life in exchange for a favor. This leads to a whole new set of adventures as he tries to fulfill his end of the bargain while also dealing with the fact that he'll now live forever.
Well, Orochimaru's immortality would mean that his influence would be long - lasting. He could continue to conduct his unethical experiments over a very long period. This might lead to the creation of new and dangerous ninja techniques or even new forms of life. In the long run, it could change the way ninja are trained and how the ninja world views power and knowledge. For example, some might start to see immortality as the ultimate form of power and strive for it at all costs. Naruto and his friends would have to constantly be on guard against Orochimaru's schemes.
On the other hand, it could cause some strain. Maybe Sasuke would start to feel trapped in this eternal existence with Naruto and long for some solitude. Or Naruto might feel that Sasuke is becoming too distant because of their immortality. However, in the end, they would likely work through these issues because of their deep bond.
Naruto's character could become more patient. With immortality, he has all the time to wait for things to develop. For example, instead of rushing into a fight, he might wait for the perfect moment. Also, his view on life and death would change. He would no longer fear losing his loved ones in the same way as he knows he can't die. This could make him more empathetic towards those who are afraid of death.