In a fanfiction like this, Orochimaru could train Naruto in the ways of stealth and assassination, skills that Orochimaru is quite proficient in. Naruto would initially be hesitant but realizes that these skills can be used for good. For example, to infiltrate enemy bases and gather intelligence to prevent wars. This would change Naruto's fighting style and make him more versatile in the shinobi world.
Naruto could be related to Orochimaru in a fanfiction through a family - like bond. Maybe Orochimaru has a past connection to Naruto's family that was previously unknown. It could be that Orochimaru had a debt to Naruto's father or some other relative, and this leads to an unexpected relationship where Orochimaru feels obliged to protect or guide Naruto in some way.
Well, it could start with Naruto getting some crucial information about the Akatsuki's next move. So he embarks on this hunt. Along the way, he could face moral dilemmas, like whether to spare some Akatsuki members who might have a sad backstory. He also has to deal with the fact that the Akatsuki are very powerful and cunning, and he has to constantly outwit them.
Sakura and Sasuke are very likely allies. Sakura has her medical skills and combat abilities, and Sasuke, despite his past issues, has great power. They've been comrades with Naruto for a long time.
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.
In this kind of fanfiction, Naruto might have used his new and powerful jutsu that he developed secretly. Maybe it was a super - enhanced Rasengan with some special chakra nature added to it, which was strong enough to overpower Orochimaru.
Since Orochimaru had many experiments and secrets, his death at Naruto's hands in the Chunin Exams fanfiction could lead to a scramble for his research. Other villages or even some rogue ninjas might try to steal his notes and facilities. In Konoha, Naruto might be pressured to reveal what he knew about Orochimaru's plans and secrets. This could put him in a difficult position as he may not know everything. Also, Sasuke, who had a connection with Orochimaru, might have a complex reaction. He could be angry at Naruto for killing Orochimaru, or he could see it as a sign of Naruto's strength and be motivated to become stronger himself.
You could look for fanfictions on platforms like FanFiction.net or Archive of Our Own. Try searching with the exact phrase 'Orochimaru trains Naruto' and then filter through the results to find ones that are well - written. Some might focus on Orochimaru teaching Naruto forbidden jutsu in a way that doesn't corrupt him but instead enhances his abilities.
It could develop in a very complex way. Maybe at first, it's full of hostility as Orochimaru has his own dark motives. But as the story progresses, Naruto's positive influence might start to change Orochimaru's perspective a bit.