Why did Χ and Ψ have such different sounds in early Eastern and Western Greek? Which sounds are older? If the Western, why were both Ξ and Χ created to denote [ks] (note that they both appear in the earliest Etruscan alphabet)?
Actually, Ξ was imported from the Phoenician alphabet (samekh, probably [s] – Smitic has a plethora of sibilants compared to Greek, so letters could be recycled for other purposes). But Ξ was not used in all dialects. Ψ and Χ were possibly created within Greek. The problem was the need to have some way to denote [pʰ tʰ kʰ ps ks], which could be done with digraphs, with distinct letters, or just ignoring the distinction. For some reason, Phoenician Ṭēt was uniformly pressed into service for [tʰ], but [pʰ kʰ ps ks] were dealt with differently by the dialects. It is speculated that X and Ψ were variants of the same letter, and in Western Greek it seems to be a simplification of ΧΣ (kʰs). There is a limit on how precise an answer to an ancient "why" question can be given: there is a need, there is a resource, people in one area made one decision, those in another area made a different decision.