Dumbledore, even if not in person, could have left behind some clues or resources that help Harry. Also, the Order of the Phoenix members who are still around and believe in Harry's cause. They have their own skills and connections that could prove useful. For example, Moody could teach Harry some advanced defensive magic techniques to use against the Ministry's security measures.
Some of the Hogwarts professors might assist Harry. Professor McGonagall, for instance, has always been protective of Harry. She could use her position at Hogwarts to cover for Harry's activities when he is away from the school on his revenge - seeking missions. And Neville, who has grown into a strong and brave wizard, could also be part of Harry's team, using his knowledge of Hogwarts' secrets to their advantage.
One possible plot could be that Harry discovers some deep - seated corruption within the Ministry. He starts by gathering evidence secretly. Then, he uses his skills and the help of his friends to expose the wrongdoings in a very public way, perhaps through a magically - enhanced news broadcast that reaches every wizarding household, causing great embarrassment to the Ministry officials involved.
Betrayal is a common theme. Usually, something or someone has wronged Harry deeply, which sets him on the path of revenge. For example, it could be the Ministry of Magic turning against him or a supposed friend revealing his secrets.
Hermione would be a likely supporter. She is always loyal to Harry and if he presented her with evidence of Dumbledore's wrongdoings, she would probably side with him. She has the intelligence to help Harry strategize and find ways to expose Dumbledore. For example, she could use her research skills to dig deeper into Dumbledore's past.
Ron might support Harry at first. Since he's Harry's best friend, he would be on Harry's side without really knowing the full story. He'd probably offer to help Harry with some of his revenge plans, like distracting Ginny while Harry sets up a magical prank.
His friends from Hogwarts like Ron and Hermione. They are always by his side and would probably be more than happy to help Harry get revenge on the Dursleys. They might use their magic skills together to create some really interesting revenge scenarios.
Perhaps he uncovers some major corruption or inefficiency in the Ministry. So, as a result of his efforts to reform it, he is given control. For example, if he finds that the Ministry has been misusing magic for personal gains, he could lead a movement to take it over and run it in a more just way.
Hermione could be a key character. She is always by Harry's side, and her intelligence and knowledge of the wizarding laws would be invaluable in the lawsuit. She might be the one doing all the research and preparing the legal arguments for Harry.
Ron and Hermione are almost surely his allies. They've always been by his side through thick and thin. Hermione's vast knowledge of magic and Ron's loyalty and courage would be invaluable in a mission to destroy the Ministry.
His friends like Ron and Hermione could be his allies. They have always stood by Harry and if Harry believes that Dumbledore has wronged him, they might side with him. Ron, with his loyalty and Hermione with her intelligence could help Harry plan and execute his revenge. They could use their knowledge of magic and Hogwarts to find ways to undermine Dumbledore's influence.
Maybe Harry uses magic to make their house a mess. He could turn Dudley's room into a pigsty or make Aunt Petunia's precious china float and then smash. It's his way of getting back at all the years of mistreatment.