The informal ones: Cranky, Mean
The in-between ones: Touchy, Sensitive
The formal ones: Irritable
It might be a bit weird to put "mean" in the informal section, but in all my time working in a professional or academic environment, another word is usually used in its place.
I've never heard anyone use "cranky" except for parents talking about their kids, or when it's someone from an older generation.
"Sensitive" is a decent word, but I put it in the "in-between" section because I use it either way. An HR representative in a company would say something, but I also might joke with my friends by saying "Someone's a bit sensitive today." It's probably the best word that you can use at any time in this context.
Personally, I don't use "touchy" and never really hear it in any situations. It could still work, but it would be uncommon to hear. I put this word in the "in-between" section because I honestly don't know where it would fall, because I just don't hear it enough.
I never use "irritable" in casual conversation with people, unless we're actively describing someone's personality. For example, I (or someone else) might say "Jane is usually irritable in the winter", but never something like "Wow, you're being irritable today."
My personal recommendation would be to use irritable if you were going to describe yourself to someone, and sensitive for any other time.