V-う/Adj-い + はず + だ, Na-Adj + な + はず + だ, N + の + はず + だ: something/someone (else) is expected to ~ ["should", not wish, desire or the like]
V-う/Adj-い + よう + だ, Na-Adj + な + よう + だ, N + の + よう + だ: "it seems that", "it looks like", "it appears to" [coloquial version - みたい, minus な or の; N version is also used as simile, "~ like N"]
V-う/Adj-い/Na-Adj/N + らしい: "it seems that ~", etc., based on what you've heard or read, as opposed to よう which is base more on first-hand information [N version typically signifies widely accepted ideas associated with N]
V-ます - ます + そう + だ, Adj-い - い + そう + だ, Na-Adj + そう + だ: conjecture based on what is seen or felt
V-う/Adj-い + そう+ だ, Na-Adj/N + だ + そう + だ: hearsay
のだ, んだ: explanationary sentence involving shared information, or inviting the hearer. Or something. It's probably about as subtle as でしょう is actual use.