Keep an eye on who gets screen time. Yes, you're going to devote time to your original character, especially if s/he really does kick ass. But make sure to give input from the canon characters as well. If you have your original character kicking ass and the canon characters standing around like a bunch of useless chumps, it's really not fair to anybody. Let the canon characters help out, even if it's your original character's mission. Distribute the lines and the action a little more.
If you really have to, go back to the very basics and figure out which stereotypical role each of the characters in the scene plays, and divide it up that way -- in Potter fandom, Harry is the hero and the jock, Ron is the sidekick, and Hermione is the brain. Your original character might be the crazy one, or another brain, sidekick, or hero/jock. Figure out what has to happen in the scene, and who has to contribute what part of it. Is that an idea that comes from a Brain, or does it come from a Lunatic? Certainly the characters won't stay within their stereotypes, not if they're sufficiently well-developed characters, but it's a place to start.
Having the characters go outside of their basic stereotypes provides depth of character, and establishing why they're deviating from the things they ordinarily do adds character development, but straying too far from the character outlines given in canon without some really super suspension of disbelief leads to accusations of taking them too far out-of-character. (If you have to take them too far out of character to establish what you were trying for in the fic, the characters may actually be telling you that they'd like to move into their own original universe, or at least get new identities and turn into a bit of spinoff fanfic rather than main-storyline fanfic.) Redistributing lines may mean that your original character loses a large percentage of action and dialog, but that actually may help strengthen the character and the story (and get you better reviews).
If one of the canon characters is present, but contributing virtually nothing to the conversation, why is that? If your original character were absent from the scene, would that character still be off in their own world, or would they be doing something else? If your original character is twice as smart as Hermione, and drop-dead gorgeous, and is taking over the things that Hermione would have been saying in the same situation if the OC weren't there... do you really think Hermione is going to take this lying down? She might be off sulking there, or she might be spoiling for a gigantic screaming bitchfight, but she's probably not going to be standing there mute and expressionless while your original character hogs the spotlight.
Figure out the group dynamics. Some things aren't going to change -- Ron and Hermione are going to play off each other, Ron is going to be protective of Harry and defend his friendship with Harry against anyone trying to take up too much of Harry's time and attention, Hermione is going to try to mother the boys a bit and keep them out of trouble. Some things are going to change. If your character wants to be Harry's new best friend, Ron is probably going to loathe your character, and Ron is probably also going to be a bit of a dick to Harry, especially if Harry is giving that character more attention than he is giving Ron.
Even if the world you're working in involves magic, human interaction patterns won't change all that horribly much. Not all characters are going to react the same. Hermione would probably shrug it off if someone were making close friends with Harry, as long as she thought that person was all right and wouldn't lead to Harry's getting in more, worse, trouble. If that person tried to become Harry's research/idea person, Ron would probably shrug it off, but Hermione might feel threatened -- or they might become the best of friends and bounce bright ideas off each other.
One of the reasons for not giving canon characters as big a say as they probably should have is not being comfortable writing the characters, or knowing that you write that particular character awkwardly, for whatever reason. So you know you have these characters to work with, so you include them in the scene because they're there -- and then do nothing with them, so it's like they're standing there with nothing to say or do. This isn't a good scene to be setting up. Either they should be there in the scene, and have a voice, and do things, or they shouldn't be in that scene at all. Figure out which way you want to take it -- either find something for them to do there, or find something for them to be doing somewhere else, and get them out of that scene so you don't have to deal with them.
If a character's thoughts and reactions are nothing like mine and I haven't the foggiest how they'd actually react to a situation like that, I don't take my chances on guessing about it! I check in with a friend, especially if I have a friend who identifies strongly with that character. I get their input on how the character would probably react in a situation like that, and I reconcile that to my understanding of the character and what's going to actually work in the story. This can also help with the problem of all of your characters acting too much like each other.
But what if your original character just refuses to behave? What if they are the hero of the story, and there are only a few very minor things that the canon characters are actually doing, and any more involvement from the canon characters would ruin the story? Then, my friend, you may well have a budding piece of original fiction on your hands. Polish the original character, find a new supporting cast that fills those same roles as the old canon's characters, and start looking about for an original universe that will suit.