It's far more common than outright Immunity, and it is easier to handle in missions.

The first such character was Elrond, by reason of his wisdom and his ring of power. Gimli is often ignored in badfic.

OOC Resistance comes from several sources:
--The character is not "hott" enough to be focused on by fanbrats and is simply ignored. Gimli the dwarf was one of the first established to be resistant because of this.
--The character is a minor character who is often present, but usually ignored. Gaspode, for example.
--The character is particularly perceptive or mentally resilient. Batman and Sherlock Holmes are both slightly resistant, though for them it may be more that they are capable of taking even the smallest traces left behind by agents and putting together two and two very quickly when they see more evidence of agents being around.
--The character is mildly insane--just nutty enough to entertain the idea that something like badfic could exist, and just sane enough to think straight about it. Murdoc from The A-Team, for example.
--The character is very genre-savvy and regularly breaks, or approaches breaking, the fourth wall. Elan from "Order of the Stick" would probably take agents' presence in stride as yet another feature of the story he knows he lives in.

OOC-resistant characters will usually be aware that something is off, and will struggle against possession or Suefluence, though usually not with much success. The benefits as far as your agents are concerned is that these characters are less likely to see them as enemies, more likely to understand that something is wrong and that the Sue is dangerous.

But you don't *have* to make such characters resistant. Sometimes it's funnier if they're not. Resistance is on the border--if the Sue is bad enough or the crossover is tangled enough, their resistance can get overwhelmed and they can go as badly out of character as you like. That's the beauty of OOC resistance instead of immunity; it gives you more flexibility with what you can do with the characters, rather than just forcing replacements.

If a character can't be neuralyzed, there are other options. Many magical and technological verses have memory-modification tech or spells. Harry Potter-continuum spells are probably the best bet unless the target is immune to magic. If it has a nervous system, some form of technology can probably do it.

And if you can't do any of that, then the agents might run around getting rid of everything else that doesn't fit and hope the canon itself gives them a hand.

I think it's kind of funny when agents get in way over their heads and have to solve a problem they never realized they were going to have to solve, like neuralyzing a creature that doesn't have a physical body.

...OOC Resistance, though?

Because I know DawnFire's got a mission where the TARDIS is character replaced, and it'd make for an interesting "Doctor's Wife"-esque mission to try and find the real TARDIS and get her back into the right place.

As I see it, the TARDIS is aware of the PPC agents and has a degree of resistance to OOC because of that power, and SUEDIS is just fun to bandy about.

Mata Nui contains the Matoran Universe inside his original body, but he isn't the entire canon. The Matoran Universe is just the main location that most of the canon-native species are from. It's not really the whole continuum; there are other planets and locations outside of it, but it's all that the main species, the Matoran, know, thus the name. Mata Nui, when controlling the Matoran Universe, has the power to bestow life to new species, manipulate the land and gravity inside the Matoran Universe, and control the destinies of beings born within the Matoran Universe, so that's pretty godlike, at least in my opinion. When the story advances, he loses the Matoran Universe body, and the nigh-on-divine status that goes with it, and would thus lose the OOC Immunity. It's sort of like the reverse of what happened to Madoka from Puella Magi Madoka Magica, who gained OOC Immunity by ascending to godhood.

Rule of Funny should still come into play for whether or not Mata Nui-as-Matoran Universe remembers them, though. That's always best.

When you brought up Q, I suddenly realized how awful a time agents would have killing a replacement for just about anything in the Q continuum. Other than getting another Q to remove its powers, there'd be little that could weaken it, and charging it would draw its attention long enough for it to teleport its assailants into space. I do not envy the agents who first encounter one.

I must say that this is a complex bit. As with most of the other replies, I would say it depends on what exact point this is in the canon.

If, for instance, the fic is set in the first two years, Makuta Teridax would be a being of god-like power, but he would have a physical form. At the end of the second year (Nuva storyline, I believe) that's when Makuta's body is destroyed in a very complex string of events (involving being turned into a mutated combination of Toa and Makuta, and then getting squashed) and he becomes a malevolent cloud of gas.

But, if this is set in the Metru line, which is a prequel to the first two lines, then Makuta is back in his old physical form.

After the climax of the Nuva line, Makuta remains a cloud of gas until after the Mahri line, at which point he takes over the Mata Nui robot and ejects Mata Nui inside the Mask of Life.

Then during the climax, he gets his head busted in by a falling moon.

So yes, in culmination, it would definitely depend on what line of Bionicle this is. (And yes, I'm also an extreme Bionicle nerd.)