In the long run, Percy might grow from the experience. He could become more cautious in his relationships and less trusting. Or, if there's a chance for redemption in the fanfic, he might be open to forgiving Annabeth if she shows true remorse and has a valid reason for her actions. But initially, it would be a very difficult and emotional time for him.
At first, Percy would likely be angry. He has faced so many challenges with the belief that his father was on his side. The betrayal would make him feel like all his efforts were in vain. He could lash out, perhaps even using his powers in a more reckless way. But as time goes on, he might start to question if there's a deeper reason behind Poseidon's actions and try to find out the truth, especially if he still has friends who believe in him and encourage him to look deeper.
Percy would be extremely hurt. Sally is his mother, and her betrayal would shatter his world. He might initially go into denial, not wanting to believe that she could do such a thing.
Another way Percy could react is by giving Annabeth the silent treatment. He wouldn't talk to her for a while, which would be really difficult for Annabeth as they are usually close. Percy would just go about his business, ignoring her attempts to communicate until he feels she has truly understood how much she has angered him.
Then, she would probably be angry. Annabeth is a strong - willed character. She would feel betrayed and used, and her anger would fuel her to find out the truth. She might start her own investigation to figure out what's really going on with Percy, whether he's been influenced by someone or if there's another reason for his actions.
Issei would probably first try to understand why Rias has betrayed him. If he finds out that she was forced or manipulated, he might try to save her. But if it was a conscious choice, he could become angry and vow revenge. He has a strong will, and this betrayal could fuel his determination to become stronger on his own.
At first, Naruto would likely be extremely shocked. He has always considered Sakura a friend and teammate, so this would be a huge blow. He might question his own judgment in trusting her.
Percy's reaction could be complex. Initially, he'd be hurt and angry. But as time passes, if Annabeth is sincere in her attempts to get him back, he might start to question his own feelings. He could be torn between his love for her and the pain of the betrayal.
Cap would be shocked at first. He trusts his comrades, and for the Clint team to betray him would be unexpected. He would likely feel a sense of betrayal and anger. He might start by trying to isolate the situation, to keep the knowledge of the betrayal from causing too much unrest in the Avengers. Then he would try to find a way to stop the Clint team from causing more harm, whether through negotiation or combat.
Percy's reaction could also be one of self - doubt. He may start to question his own actions and leadership. He might think that he has done something wrong to push Annabeth away. However, his loyalty to his friends and the cause would eventually make him stand up against Kronos and try to bring Annabeth back to the right side.
He'd probably be devastated. Percy loves Annabeth deeply, so this would be like a punch in the gut for him.