Well, in fanfiction, if Thor kidnapped someone, it would be a huge deviation from his normal heroic character. It could be that he's trying to protect the person from a greater danger in his own, misguided way. Or perhaps he's been tricked into thinking the person has information vital to Asgard's safety. This situation would definitely shock his friends and allies, and would probably make for a very interesting and complex fanfiction story.
Well, in this kind of fanfiction, Sonic might be held in a strange and dangerous place. His friends like Tails would surely start a rescue mission. They could search all over the Sonic's world, facing various obstacles on the way. Maybe the kidnapper has some evil plan related to Sonic's speed or his Chaos Emeralds.
Well, it could also be a very emotional and character - study type of fanfiction. Thor chokes Tony not really out of hatred but out of deep - seated fear. He might be afraid that Tony's actions will lead to the destruction of everything they hold dear. And this act of choking is more like a wake - up call for Tony to realize the gravity of the situation.
Well, perhaps Percy would initially mistake Thor for a new kind of demigod. Thor, on the other hand, would be intrigued by Percy's unique skills. They could exchange stories about their adventures. Percy would tell Thor about his quests in the Greek world, and Thor would share his tales of Asgard. And in the end, they might become friends and even learn new combat techniques from each other.
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 a 'Katniss and Peeta kidnapped' fanfiction, they could be taken by a group of outlaws who want to ransom them back to District 13. During their captivity, Katniss and Peeta might learn more about the outlaws' motives, which could be more complex than just money. They could also use this time to plan their own rescue, using their skills from the Hunger Games.
In a fanfiction like this, Bumblebee could be kidnapped by a powerful alien race that has a vendetta against the Autobots. The kidnappers might subject Bumblebee to various forms of torture to break his will. However, Bumblebee's strong spirit would keep him from giving in. His Autobot comrades would eventually come to his rescue, engaging in an epic battle against the kidnappers.
In this fanfiction, Ichigo might be held in a secret location by Aizen. Aizen could be planning to use Ichigo for some dark experiment or to gain his power. Maybe he'll try to manipulate Ichigo's Hollow side for his own evil purposes.
Well, in such a fanfiction, Sakura might be used as a bargaining chip. The Akatsuki could try to exchange her for something valuable, like secret jutsu. Or they might want to extract information from her about Konoha's defenses.
In this kind of fanfiction, Robin might be in a lot of danger. Slade could be using Robin to get to Batman. He might try to brainwash Robin and turn him against his friends. For example, he could lock Robin in a secret lair and show him false information about Batman to make Robin question his loyalty.
In the 'ichigo gets kidnapped fanfiction', he might be rescued by his friends. For example, his comrades from the Soul Society could sense his distress and come to his aid.