«Который» ("that/which") is like an adjective, only it takes the gender of whichever object it "represents", and the case that corresponds to its role in the part of the sentence you use it in:
кто-нибудь and что-нибудь mean a "hypothetical" object. A slot you have in mind, not actually filled by anything in particular (and maybe you are wrong). Mostly useless in statements about the past (if you are sure it happened, then the object did exist)
кто-то and что-то refer to a specific but "unknown" object. You see/know that something exists (or you are sure of it) but you don't know its identity.
They are somewhat interchangeable when you mean there's free choice from a limited number of options ("OK, have someone call me if Alex comes").
NB: "any-" pronouns have wider use in English. When "anyone" means "whichever person you want", consider "кто угодно" or, if you mean everyone, "все". The above only applies to cases of an "unknown" object.
Кое-что and Кое-кто are "secret" pronouns. They mean a certain object that you know but are deliberately not mentioning by name. Either you want to keep people guessing or do not consider the identity important to your point ("Yeah, I have worked with some people* here").
Когда-нибудь is used mainly for "ever" in the past or "one day" in the future. Когда-то is mostly for "once" in the past; almost never used in future.
Как-нибудь is also sometime used to refer to some future moment rather than manner of action.
Где-то is also used colloquially to mean "approximately*.
Кое-как is only an adverb, which either means a job done sloppily or an action performed "barely", with difficulty.