Another scenario could be that Orochimaru has some information that Naruto and Hinata desperately need. So they make a deal with the devil, so to speak. This could lead to a lot of internal conflict for both of them, as they are allying with someone who has done so many heinous acts in the past.
In a fanfiction where Naruto and Hinata join Orochimaru, one possibility is that they are forced into it. Maybe Orochimaru has some kind of leverage over Konoha that makes them comply. Naruto, being the head - strong character he is, would likely be constantly looking for a way to escape and take Hinata with him. Hinata, on the other hand, would probably be more reserved and observant, trying to find Orochimaru's weaknesses.
In a fanfiction where Naruto and Hinata join Kumo, one possibility is that they are sent there on a diplomatic mission that turns into a permanent stay. Naruto's charisma could win over the Kumo villagers, and Hinata's Byakugan would be a valuable asset. They could work together to reform some of Kumo's more archaic shinobi practices. Naruto could also train with the Kumo ninjas, sharing his sage mode knowledge, while Hinata could teach them about the Hyuga clan's gentle fist techniques.
One possibility is that Naruto discovers Orochimaru's lair through some clever detective work. He then sneaks in, avoiding all the traps. When he sees Orochimaru about to perform some sort of experiment on Hinata, Naruto jumps in and starts fighting. He might transform into his Nine - Tails Chakra Mode to gain an edge in the battle and save Hinata.
In a scenario where Orochimaru kidnaps Hinata, the Hyuga clan would surely get involved. They'd be outraged and use all their resources to find her. Orochimaru might be interested in Hinata's Byakugan for his experiments. He could try to extract its power or study it. But Hinata has been trained in the Gentle Fist style, so she might be able to hold her own against Orochimaru's minions for a while. And who knows, Sasuke might also get involved. He has his own history with Orochimaru and might see this as a chance to confront him again, especially if he realizes that an innocent like Hinata is in danger.
On the other hand, their relationship could also grow stronger. They would be relying on each other more in this new and dangerous situation. Naruto would be even more protective of Hinata, and Hinata would be a source of comfort for Naruto. They would have to communicate and trust each other more deeply to survive in Orochimaru's lair.
Well, in such a fanfic, Naruto joining Orochimaru would be a huge shock to the Naruto -verse. Orochimaru has always been an enemy, so for Naruto to side with him would mean a major shift in the power dynamics. Naruto could learn a great deal about the darker side of the ninja world, but he'd also be in constant danger of being used by Orochimaru for his own purposes. It would be a very different Naruto story, full of moral dilemmas and unexpected alliances.
Well, Naruto could potentially be used as a bargaining chip by Orochimaru. Orochimaru might try to trade Naruto for something he wants from Konoha, like secret jutsu scrolls or some kind of political power within the village. And Naruto, being the determined hero he is, would likely be constantly looking for a way to escape and foil Orochimaru's plans.
In some fanfictions, Naruto might go to Orochimaru seeking power. He could be tempted by Orochimaru's knowledge of jutsu. Maybe he thinks that by learning from Orochimaru, he can become stronger faster and be better able to protect his friends and the village.
Well, if Sakura and Hinata join the Akatsuki, it would be a total chaos. The Akatsuki is a group full of outlaws and anti - heroes. Sakura's combat skills and medical ninjutsu could be used in new and unexpected ways. Maybe she could try to heal some of the Akatsuki members who are on the verge of death. Hinata, with her gentle nature and Byakugan, would be an interesting addition. She might use her Byakugan to spy on the Akatsuki's enemies or help them plan better strategies. However, they would also face a lot of internal conflicts within the Akatsuki as not everyone would trust them easily.
Well, Naruto might use his Nine - Tails chakra to break free. He's a tough one. He could also try to outwit Orochimaru with his ninja skills. Maybe he'd pretend to be unconscious and then surprise Orochimaru when he least expects it.
In the fanfiction, Naruto being taken by Orochimaru could lead to a whole new set of character developments. For one, Naruto's view of the ninja world might change. He's used to the relatively 'good - guy' environment of Konoha. But with Orochimaru, he'd be exposed to the more underhanded and cruel aspects of the ninja world. His relationships with his friends could also be put to the test. His friends would surely try to rescue him, and Naruto would have to decide whether to rely on them or try to handle things on his own while in Orochimaru's clutches.