In what order are application materials read by admissions officers at University of California? I ask because different application materials will reach them at different times - like Letters of Recommendation etc.

They do not necessarily follow an order. Each campus evaluates 14 factors differently. You would need to check the website of each campus to found how they use the 14 factors. The 14 factors are listed here along with links to each campus admissions page: https://admission.universityofcalifornia.edu/how-to-apply/applying-as-a-freshman/how-applications-are-reviewed.html.