Is anything known about whether {nay} and {Saw} are transitive and/or
intransitive, or how they are used?

Specifically, are they "marry" in the sense of "get married"
(intransitive) or "get married to [person]" (transitive)?

Given http://www.qephom.de/e/message_from_maltz_170713.html and its
endorsement of the grammaticality of {naychuq} and {Sawchuq} and its
example of {B tlhogh A}, I assume that {nay} and {Saw} work similarly
and that one can say {qeylIS nay luqara'} and {luqara' Saw qeylIS}.

Any Klingon verb that can take an object may leave that object off to mean either the action is done in general or to an unspecified object. So nay luqara' means Lukara marries (in general, or someone unspecified).

I didn't doubt before that those words took objects; allowing -chuq on them cliches it for me.

-- 
SuStel
http://trimboli.name