She may start by trying to figure out who the kidnapper is and what his motives are. If she has any special abilities or skills, she would be thinking about how to use them to her advantage. For example, if she has telepathic powers, she could try to send a distress signal to her friends or family. Also, she might try to gain the kidnapper's trust in order to find a moment to escape.
One possible plot is that the guy in the van is actually under the control of a more powerful villain. The anime girl, who might be a key figure in the anime's lore, is kidnapped to be used as a bargaining chip. However, during her captivity, she befriends a small creature or another captive in the van. Together, they come up with a plan to escape and expose the real villain behind the kidnapping.
Maybe the guy in the van has a personal vendetta against Sango. He might be someone from her past that she wronged accidentally. In the fanfiction, Sango could use her combat skills to try and escape the van when the kidnapper least expects it.
Sakura would probably be initially terrified. She would try to use her medical ninjutsu skills to defend herself or at least slow Itachi down. If she realizes she can't overpower him physically, she might try to talk to him, asking him why he's doing this.
She would be terrified at first, but quickly gather her wits. Hermione is very intelligent, so she would likely start observing her surroundings, looking for any possible means of escape or a way to send a signal to her friends.
Some Avengers might be really confused at first. For example, Tony Stark would probably be intrigued yet find it a bit odd. He'd be analyzing it like he does with new tech, trying to understand the appeal and the different universes within the anime fanfiction.
She could be held hostage in an abandoned building. The kidnapper might demand a ransom from her friends in the anime. Her friends would then have to figure out how to get the money and rescue her without getting caught by the kidnapper's traps.
Peter would probably be really confused at first. He looks up to Tony, and suddenly being kidnapped by him would be a huge shock. He might try to talk to Tony, asking him why he's doing this.
Hermione would be extremely worried and would start researching like crazy to find out where Dumbledore has taken Harry. She would probably suspect that something is not right with Dumbledore and would try to convince Ron to help her. Ron, on the other hand, would be initially shocked but then would be ready to go on a rescue mission with Hermione.
At first, Harry would be in shock. He would be full of disbelief that Dumbledore, of all people, would do such a thing. He would struggle both physically and emotionally. Physically, he would try to break free from whatever bindings or magical restraints Dumbledore has put on him. Emotionally, he would be a mess, feeling hurt, scared, and confused. However, depending on how the story unfolds, he could gradually come to terms with the situation if Dumbledore manages to convince him that it's all for a greater good.
Gon would probably be angry at first. He has a strong sense of justice and being kidnapped against his will would surely make him mad. He'd try to fight back immediately if he had the chance.