My story has a group of five refugees traveling across the kingdom. One of them is preachy and pretty much useless (unused to physical labor, trying to convert the heathens in the group). She's driving three of the others (including the MC) completely crazy.
How can I show that she's turning the other characters into giant flaming fireballs without annoying the reader as well?
I'm assuming I should keep her dialogue to a minimum...
You need to get inside her head. Everyone makes sense to themselves. She has reasons for doing things and, you might disagree, but they're valid to her. She has goals and dreams and desires. She has conflicting emotions and strengths and weaknesses.
If you show her like you described her here, she is a shadow of a character. A stereotype. I find reading about a stereotypical character far more annoying than any character can be in the first place.
The most annoying character in the world, however, can be a joy to read in the hands of an author who understands her.
Of course, even the great characters can be too much if you overuse them. And too much dialogue is wearing for a reader. So balance things. And if you don't want this character to be a main character, that's fine. Don't use her very often. But treat her like a human being (or alien or whatever) with the same worth as everyone else. Your other characters can be annoyed as all get out by her, but your reader should enjoy reading about all your characters.
Call her Marie. One way is to let a few other characters (Mike and John) express their frustration with Marie when she is not present; and actually laugh with each other by exaggerating and joking about her.
This is what we do IRL, rather than express any direct hostility toward the irritating person and create a real rift, we find some catharsis and release by laughing about how over the top and irritating she really is.
This creates an inside joke between two characters, one the reader is in on; so when Marie makes some otherwise mildly preachy observation, you can put a spotlight on it: Mike looks at John with a pained look and wide eyes, John bursts out laughing, and Marie is interrupted.
"What's funny?"
"Nothing," John said, "I was just remembering this stupid thing. Please, go on, Mike is dying to hear the rest of your story!"
"Oh, how sweet!" Marie said, turning to John, "I'm so glad you are interested!"
You can even use this as a step toward two strangers (Mike and John) bonding as friends. The only risk here, if you choose to realize it, is that Marie finds out they are making fun of her.
You don't have to let that happen, but if you choose to, you can handle that as a character growth opportunity for any of the three. For example, say John is actually a nice guy. Marie finds out they have been making fun of her, and retreats to cry. In his attempt to apologize, he learns her religion is adopted, and out of fear; it comforts her and makes her feel safe in an inherently unsafe world. Mike's attitude may be "She needs to get over it, the world is a dangerous place."
But John can develop sympathy for Marie, and become protective of her. His solution to avoid the religious talk is to talk to her about other things. Perhaps they even fall in love. Now they both have character arcs.
One technique you could use is to demonstrate the annoying-ness of the character by making the other characters reactions show their annoyance. What the other characters find annoying need not be annoying to the reader, the reader might even appreciate it. For example, frequently asking questions that "should be obvious" but that the reader might not know otherwise. Or critiquing other characters in a way that sheds light on that character and helps develop them. Complaining about something that the reader would not otherwise know was a problem. Comedic relief to break the tension.
Other characters reactions can be varied, as long as they show annoyance. Simply ignoring this character might work sometimes, complaining to each other about her obnoxiousness, telling her to be quiet -- as long as it makes sense for their character. This is the part that is really going to make the reader understand that your character is annoying, so focus the details here rather than on the annoying person herself.
You'll see a good example to learn from when protagonist Ralph meets Vanellope in Wreck-It Ralph.
She annoys him partly because of a short-lived immature aping of his words, but mainly because she obstructs his ability to recover a medal he rightly earned, and which he thinks he needs to get his colleagues' respect. In his efforts to get rid of her he tells a number of lies and makes a fool of himself. It doesn't cost him the audience's sympathy, but nor does all our moral condemnation fall on her. And we quickly learn she takes the medal because of an serially even greater personal need it can fulfill. You might say a problem shared is a problem halved.
I don't want you coming away from this thinking this only works with children annoying adults. I could have discussed an example reversing those age roles in Coco with the Miguel/Héctor dynamic. I'll leave you to find child, adult-adult, Wookie-droid etc. examples of his own.
I am not a writer so please don't expect a great answer, but think of characters Kristen Wiig played on Saturday Night Live (SNL). Some of the most annoying characters she played were adored by audience. “Target Lady”, “Secret Word”, “Thanksgiving Soup kitchen”, “1920's party” etc. to name some. I think observing the traits of those characters can help.
