I've never looked into it, Tori-kun, but I imagine that it just represents grammaticalization of usage over time and there's isn't any particular coherence behind it. I think you just have to treat it as vocab, make a point of noticing when you read and perhaps do some targeted study.
For eg, you could put a little reminder on your cards of nouns that can be used as verbal nouns, na adj, no adj and adverbs. I believe you've been using Rachel's CorePlus deck which I believe has a field for Edicts parts of speech, so that would be easy to do. As niwasaburo mentions, though, it's sometimes difficult to classify words. Just b/c they are listed as nouns, doesn't mean the behave exactly as regular nouns do. (eg. X 特別を)
I suspect the number of no-adjs is small relative to na adjs, so you might consider searching and tagging them so you be familiar with which are both and which are only no-adj. (If you do, perhaps you could let us know? I'm curious to know how many are considered common.)
I don't know how accurate edict's POS labels are, though. For eg, 本当 is labelled as adj-na and n, but 本当の is correct, not 本当な.
Quote:I often get confused with whether using the な or の after adj-na....
Just in case: の wouldn't be an option after any na adj - only after words which are also no adj. And some words are only no adj (not na adj.)