Sirius would likely be extremely angry. He already has a protective streak towards Harry. He might immediately confront those he suspects of the abuse, whether it's the Dursleys or others at Hogwarts. He would probably also try to remove Harry from the situation as quickly as possible.
Well, James is a loyal friend. So, when he discovers Sirius is abused, he would most probably drop everything else he is doing to focus on Sirius. He'd be angry, not just at the abusers but also at himself for not realizing it sooner. He'd make sure Sirius knew that he wasn't alone and that he had someone who would always be there for him. James might also encourage Sirius to learn self - defense magic more intensively so that he could protect himself in case the abusers tried to harm him again.
She might be horrified and immediately take steps to protect Sirius. For example, she could confront the abuser or report it to the proper authorities within the wizarding world.
They might face magical punishment. For example, they could have their magic restricted or be sent to Azkaban if it's a really bad case. McGonagall would not tolerate such behavior and would push for the strictest punishment.
Remus is likely to be shocked and angry. He might immediately want to protect Sirius. He could confront those who are abusing Sirius or try to find a way to get Sirius out of that situation.
In the fanfic 'Malfoy's Revelation', Malfoy is paired with Harry for a project. As they spend time together, Malfoy notices some strange behaviors from Harry, like flinching at sudden movements. After some snooping around, he discovers that Harry has been abused. This new knowledge makes Malfoy more empathetic towards Harry and he tries to help him in his own way, which includes standing up for Harry against some of their mutual enemies at Hogwarts.
Well, first of all, the students would probably be shocked. His friends, like Ron and Hermione, would be extremely angry at the Dursleys. They might try to comfort Harry more often. And the school itself could start providing special resources for Harry, such as counseling or extra protection spells. Also, there could be a big change in the way the wizarding community views Harry. Instead of just seeing him as the 'Boy Who Lived', they would see him as a victim who needs support.