A plurality of nests of wasps
While I generally feel sure-footed on matters of literary greengrocery, I'm at a loss on this one. How would a pedant write a sign alerting others to the presence of nests of wasps to make other pedants maximally happy?
You can use the words "Danger!" "Wasp" and "Nest" and can suffix one or more "s" and an apostrophe to any of them or refrain from doing so, as you see fit.
I'm aware of the irrelevance of such considerations in the grand scheme of things.
Solution 1:
Danger! Wasp Nests!
No apostrophe in this case, because there is no possessive*. Here "Wasp" is an attributive noun, and therefore can be in the singular form even though there is more than one nest and there isn't necessarily just one wasp associated with each nest. "Nests" is the ordinary plural form of "nest." Nothing here should bother a well-educated pedant. (Peevers, on the other hand, can be bothered by anything, even demonstrably correct uses of words.)
*That's not to say that you can't find forms of this phrase that do use the possessive, like "wasp's nest." I'm just saying that it's not necessary to use a possessive, and avoiding it makes the situation with regard to prescriptive grammar a lot easier.
Solution 2:
We all know about greengrocers' proverbial fondness for apostrophes. But it turns out for OP's specific context, everyone prefers to include the apostrophe. The only question being whether they pluralize wasp first...
[]1
...where as you can see, usage is pretty evenly split on that point. I suppose some pedants might say because there are many wasps associated with the nest, they should be pluralized.
To summarise, a wasp's nest and a wasps' nest are equally common, a wasps nest is very rare, and a wasp nest sits somewhere in the middle. Relative prevalence has changed little over several generations.