It's possible that some of the minor gods who have an alliance or a friendly relationship with Percy might try to rescue him. For instance, Poseidon, Percy's father, would surely be enraged if he found out Aphrodite had kidnapped his son. He might send some of his sea creatures to search for Percy or even confront Aphrodite directly to demand his son's release.
Annabeth would most likely be the first one to try to rescue Percy. She and Percy have a deep connection, and she wouldn't stand by while he's in danger. She's smart and resourceful, so she'd come up with a plan to find out where Aphrodite has taken him and then figure out a way to get him back.
His other demigod friends from Camp Half - Blood could also attempt the rescue. Grover, for example, would feel responsible for Percy's safety. He might use his nature - related powers to track Percy down. And the other campers who have fought alongside Percy in the past would also join in. They all know Percy is an important part of their community and they wouldn't let Aphrodite keep him hostage without a fight.
Gale might also attempt to rescue Katniss. He's her friend from District 12 and is quite skilled in his own right. He would be furious to hear that Cato has kidnapped Katniss and would likely gather resources and allies to try and save her.
Elena would definitely be one of the first to try. She loves Jeremy and would do anything to save him. She would probably start by looking for Damon's usual hiding places.
The rest of Team 7, like Sakura. She may not be as strong as Sasuke or Naruto, but she has a strong will. She'd be worried sick about Naruto and would do whatever she could to help in the rescue. Plus, she might be able to use her medical skills to treat Naruto if he's injured during the kidnapping situation.
Naruto would probably be one of the first to try and rescue Kakashi. He has a strong bond with Kakashi and would not stand by while his teacher is in danger.
Sasuke might also be involved in the rescue. Despite their complicated relationship, he still has some feelings for Sakura. And he wouldn't want to see her in the hands of someone like Deidara. Also, Kakashi, as their former sensei, would likely lead a rescue mission. He has the skills and experience to deal with Deidara's explosive attacks and find a way to save Sakura.
Naruto would surely be one of the first to try and rescue Sakura. He has always been protective of her and would not stand by while she's in danger.
The Salvatore brothers, Stefan and Damon, are the most likely candidates. They both have a strong connection to Elena and would stop at nothing to rescue her. Stefan's sense of chivalry and Damon's fierce protectiveness would drive them to track down Katherine and get Elena back.
Well, perhaps Aphrodite kidnaps Percy because she wants to play matchmaker. She might see some potential love connection for him that he's been avoiding, so she takes matters into her own hands. Maybe she has a grand plan to set him up with a certain demigod or even a mortal, and she believes that by kidnapping him, she can force him to face his romantic destiny.
Annabeth could be a likely candidate. She's always been by Percy's side, and she'd stop at nothing to save him. Her intelligence and combat skills would be useful in the dangerous environment of Tartarus.
Her father, Charlie, might try to rescue her. He loves Bella deeply and would be very worried when she goes missing. He could start investigating and find out that the Cullens are involved.