As a well-read native speaker, I know what “sounds right”, but I often don’t know the formal terminology or rules to explain why to a learner.
Are there any grammar books or other resources that can help me write better answers here without being either too basic for a native speaker or too academic for a casual reader?
The Cambridge Grammar of the English Language (CGEL), Huddleston and Pullum, 2002, a very often cited reference book in these here parts (ELL and ELU). I don't know remotely as much about CGEL as some knowledgeable contributors, and I only consult it and reference it when I need to, but it is one of the most comprehensive and coherent grammars. Note that from what I understand it is not without issues and doesn't always agree with other major grammar reference books.
This canonical meta post includes some other useful grammars.
Huddleston and Pullum's Cambridge Grammar of the English Language (1860 pages) is a grammar reference aimed primarily at linguists.
For mere mortals, I recommend Cambridge Grammar of English: A Comprehensive Guide by Ronald Carter and Michael McCarthy (Cambridge University Press, 2006), which is also much more affordable.
CGEL is popular with many users, but McCawley 1998 is an alternative that is completely clear and well-written (by one person), with all deviations from traditional terminology explained as they occur, and no made-up terminology. It's a generative grammar, but not a Chomskyan grammar. McCawley gives top billing to the grammatical phenomena of the title, and only second billing to the theory he uses to describe them.
One nice feature is that McCawley 1998 is available as a paperback that can be held and used with one hand.
