While the Harry Potter series as a whole is an exemplary example of the theme of "good versus evil," The Order of the Phoenix contains many additional themes. Among these are grief, coming-of-age, romance, trauma, and governmental corruption. Let's consider how each of these themes plays out in the text.
Grief is a major theme in Harry Potter and the Order of the Phoenix. At the end of the fourth book, Harry's schoolmate Cedric was murdered in front of him. Not only is Harry forced to deal with his own sorrow about Cedric's death, but many other people focus their grief on him. Harry has a crush on a girl named Cho Chang, and though she has feelings for him as well, she feels strange because she used to date Cedric. Late in the book, Harry's godfather Sirius Black passes away, and Harry is distraught because he has lost yet another guardian in his life. Harry felt Sirius was one of his only connections to his parents, and also one of the only people who really understood him as he was. Sirius's death also shatters the possibility that Harry could escape living with his terrible aunt and uncle.
The theme of coming-of-age overlaps with many other themes throughout the book. For the first time, Harry is learning to assert himself and not act only according to the will of others. He begins standing up to those who might treat him like a pawn in a game. While this gets him into some trouble at school, it benefits him in his ongoing fight against Voldemort and the dark forces. Harry's sense of responsibility and ownership over his identity really grows during the fifth book, especially as he takes on a leadership role for the Dumbledore's Army club. Ron and Hermione also take on leadership roles as school Prefects.
In other characters, namely Fred and George Weasley, we can see that some people aren't afraid to chase their dreams. Fred and George always thought outside the box and didn't really fit into the rigid structure of a Hogwarts education and Ministry career. Rather than living lives full of dissatisfaction and reprimanding, they decide to leave school and pursue something they are truly good at and passionate about.
As with most teen relationships, the theme of romance is a little awkward and uncomfortable for Harry. Harry has had a crush on Cho for more than a year, and now that Cedric is out of the picture, he would love to date her. Unfortunately, Cedric's death hangs over Harry and Cho's relationship like a ghost. When they're together, Cho cries a lot because she feels she isn't respecting Cedric's memory.
Trauma is a major theme of this book, and one I feel is very important to address. When Harry is kidnapped by Peter Pettigrew for the purpose of reviving Voldemort at the end of The Goblet of Fire, Harry has an incredibly traumatic and isolating experience. Not only is Harry held against his will, he witnesses the death of a schoolmate, experiences physical torture, faces the man who murdered his parents, and is confronted with the fact that he has developed a relationship with an abusive imposter posing as his professor. Throughout the fifth book, Harry struggles with nightmares, bursts of anger, and intense feelings of dissociation from those around him. As Voldemort has returned and projects images into Harry's mind, Harry even grows to mistrust himself. Though it is never explicitly mentioned, Harry displays many of the signs of Post-Traumatic Stress Disorder.
The theme of corruption really serves to set the scene and plot for the fifth book. The Ministry of Magic, which denies Harry's claim that Voldemort has returned, intervenes at Hogwarts in the person of Dolores Umbridge. As far as we know from the books, prior to Umbridge's appointment, the Ministry's only intervention at wizarding schools was for examination purposes. Umbridge's presence and actions on behalf of Minister Fudge show how badly the Ministry wanted to keep Harry quiet, under control, and out of its way. I think Minister Fudge knew or was suspicious that Voldemort had indeed returned, but did not want this to reflect as some sort of failure on his part, so he decided influencing the entire wizarding community to be mistrustful of Harry and Dumbledore seemed like the best course of action.
Early in the book, Harry is sent to court for producing a patronus charm to protect his cousin from dementors. At this time, at least some members of the wizarding community are sympathetic to Harry and believe what he says is true. Harry is cleared of the charges thanks to the good word of Professor Dumbledore, and he is free to return to school. As the book progresses, scathing newspaper articles tear the public image of both Harry and Dumbledore to shreds so that by the time Voldemort tries to act again, nobody believes them.
I'm sure many more themes are present and available for analysis in The Order of the Phoenix, but I feel those I've discussed here are central to the plot.