I think the word "vexed" suits Asakura simply because it's such an understatement.
I think a translator with no grasp of colloquial English usage just picked a potential meaning of "iraira" out of his J -> E dictionary at random!
Vexed has connotations in English that are
absolutely inappropriate to Asakura. I feel like his use of "iraira" would be best translated as "pissed off," since Asakura strikes me as the type to use a lot of slang and crude (yet TV-friendly) language. You could also use "annoyed" or "irritated" and they'd be reasonably appropriate.
Good English usage is all about the
synonyms, not 1-to-1 correspondence. English is a language that typically has 6 to 10 different words you can use to express any idea, each with very particular connotations that suit different moods and levels of formality. When you translate any language into English, picking out synonyms to properly convey gradations of meaning is crucial.
Here, do something for me. Pause a Ryuki episode sometime and read Asakura's dialog out loud. Go on, do it. Try to say it the way you think Asakura would. Record yourself. Play it back. You'll probably notice that your recording sounds
completely stupid.
That's a classic sign of bad dialog translation. A good dialog translation can be read out load and will sound... if not natural, like something a Westerner would write. Western TV shows
have characters like Asakura and they sure as hell aren't ever saying that they're "vexed" because
nobody talks that way.
For him to say that he's vexed when he's obviously pissed enough to chop off your head a thousand times over makes him seem all the more threatening, especially when he uses a rather nonchalant tone to underscore his inner brutality, rather than for him to state that he's pissed outright.
Two problems here. One, Asakura IS stating that he's pissed outright. That's what "iraira" means. If his dialog was meant to understate his anger he'd have an entirely different, much more circuitous speech pattern. Especially since Japanese is loaded with ways to say you're murderously angry without using terms as blunt as "iraira."
Two, when Asakura is ready to kill a guy and says he's "vexed," it makes him sound like he's bored and mildly disinterested in the action. "Vexed" is a prissy word, something you say if you're an upper-crust British lawyer who drinks a lot of Earl Grey tea. Asakura is a stone cold killer. Why is he using prissy language?
I often found the dissonance between Asakura's usually-overt tone and the goofy word choice in the translation hilarious, so I had problems taking Asakura seriously. Asakura is clearly intended as a sort of lowbrow Hannibal Lecter, the one guy who's playing the Rider Fight "correctly." He should be bluntly terrifying; no more, no less.