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 this fanfiction scenario, it's possible that Naruto's friends would quickly come to his rescue. Sasuke, for example, would be very determined to save Naruto. He has his Sharingan and his own set of powerful jutsu. Sakura could also use her medical ninjutsu to heal Naruto if he gets injured during the rescue. And Kakashi would surely lead the mission, using his experience and various jutsu like the Raikiri.
Another thing that could happen is that Orochimaru has some ulterior motive for kidnapping Naruto. Maybe he wants to extract the Nine - Tails' chakra for his own experiments. But Naruto, being the hero he is, would resist with all his might. He might even start to connect with the Nine - Tails on a deeper level to gain more power to fight against Orochimaru.
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.
One possibility is that Naruto's friends would immediately launch a rescue mission. They would likely gather intel about Kumo's motives and whereabouts. For example, Sasuke might use his Sharingan to track any clues left behind. Sakura would prepare medical supplies in case of injuries during the rescue.
In this kind of Yaoi fanfiction scenario, one possible thing that could happen next is a lot of emotional turmoil. Sasuke might have kidnapped Naruto for reasons related to his own inner demons or some misconstrued idea of protecting him. Naruto, being kidnapped, would initially be angry and confused. He would try to reason with Sasuke, leading to some intense dialogues that could explore their complex relationship. There could also be a moment where Naruto starts to understand Sasuke's motives a bit more, which might lead to a change in their dynamic, perhaps even towards a more affectionate connection as is often the case in Yaoi stories.
If Orochimaru kidnaps baby Naruto in fanfiction, it would likely start a race against time for the Hidden Leaf Village to get him back. The village elders and the Third Hokage in particular would be desperate to rescue Naruto. They might send out their best ninjas, including Kakashi, to track Orochimaru down. Orochimaru, on the other hand, could be planning to raise Naruto as his own weapon, brainwashing him from a young age to be loyal only to him.
Naruto getting kidnapped by Orochimaru would be a really dangerous situation. Orochimaru could start by putting Naruto in some sort of chakra - suppressing device. This would limit Naruto's ability to use his Nine - Tails power. Then, he might try to implant some of his cursed seals on Naruto, which would give him more control over Naruto. But Naruto has his own allies within himself. The Nine - Tails, despite their rocky relationship, might help Naruto out in this situation. Also, Naruto has the memories of all the people who care about him. He'd draw strength from those memories and keep his hope alive, waiting for the moment when he can break free and return to his friends and the village.
Another scenario could be that Naruto discovers a hidden chamber in the lab. Inside, there are test subjects that Orochimaru was using for his immortality experiments. Naruto feels sympathy for them and tries to rescue them. However, he has to figure out how to deal with the various traps and security measures in the lab first. He might call for help from his friends like Sakura or Kakashi to assist him in this difficult task.
In a fanfiction where Esdeath kidnaps Tatsumi, one possibility is that she tries to force him to join her side. She might use various means like threats against his friends or promises of power. Tatsumi, being a hero at heart, would likely resist. He could try to escape while also trying to figure out Esdeath's weaknesses to defeat her later.
Well, in a typical scenario, Sonic would probably rush to save Tails. He'd use his super speed to track Eggman's lair. Maybe he'd find some clues along the way, like a piece of Tails' fur or a gadget that Eggman accidentally dropped. Then, Sonic would face off against Eggman's badniks, defeat them one by one, and finally reach Tails. He'd free Tails and they'd escape together, with Eggman vowing revenge as usual.
Another scenario could be that Naraku has some ulterior motive for kidnapping Kagome. Maybe he wants to use her spiritual powers for his own evil purposes. He could try to corrupt her or force her to use her powers against Inuyasha and the others. But Kagome would resist with all her might, and her love for Inuyasha and her friends would give her the strength to hold out until they come to her rescue.
Well, one possibility is that Elena's friends would immediately start a search party. Damon, for instance, would be furious and stop at nothing to find her. He might enlist the help of Stefan and Bonnie. They could use Bonnie's magic to try and track Klaus' whereabouts.