For good writing, I strongly recommend Steven Pinker’s The Sense of Style alongside Zinsser’s On Writing Well. Both include concrete suggestions for avoiding/correcting common errors but are more valuable IMO for outlining a stance, maybe an ethos, for writing non-fiction. Pinker specifically describes the “classic style” of writing, which sounds weird and stuffy but is in fact (IMO) a very important way to think about writing and communication. These visions of ethos are strongly relevant to “outreach,” I would argue.
As for more general aspects of public outreach, I would urge all of us to consider the AAAS document on “Scientists in Civic Life,” which is linked with other important resources on the PS mission page.