くさい(めんどくさい) The most common, general word for annoying.   KIDS$$$
(やっかい) Close to 面倒. Someone who is hard to deal with! A hard-to-fix appliance. A stubborn, persnickety person.
煩わしい(まずわしい) An annoying process (paperwork, say) which isn’t difficult per se,  but is really time-consuming, and full of trivial rules.
ややこしい Something which is annoying because it is a difficult and confusing process, which never seems to end. You always have to do one more thing just when you thought you were done. Can also be used of a person who keeps bugging you with “just one more question.”