Punctuation following “along the lines of ”
There’s no reason to use any further punctuation than quotation marks, if those.
I'd argue that the division of reproductions of speech or text into 'direct speech' and 'indirect speech' (there are other terms used, of course) is a rather confusing practice. Collins Cobuild Grammar uses the terms 'quote structure' and 'reporting structure' and analyses the two different structures more logically. It states: When you want to say that a person [/text etc] used particular words, you use a quote structure. You can do this even if you do not know, or do not remember, the exact words that were spoken [/written / displayed]. [bolding and inserts mine]
Thus, if I may tweak the example given,
The teachers heard replies along the lines of "Must be nice to have the time for a vacation."
is a quote structure, whether or not the teachers heard the precise words contained within the inverted commas. Compare:
The teachers heard him reply, "Must be nice to have the time for a vacation."
The teachers heard the reply: "Must be nice to have the time for a vacation."
The teachers heard the words: "Must be nice to have the time for a vacation" - or something very similar. [I'm assuming I don't need to double-punctuate with a comma here - it's an unusual construction I've never met - but doubtless some style-guide will disagree, or seem to.]
Report structures (other than questions) almost always have that-clauses (from which the that may be elided) or to-infinitive-clauses. Here, a comparable report structure would run:
The teachers heard people complaining that they didn't have the amount of holidays the teachers did, and so couldn't fit in a vacation.
Modern rules for punctuating quote structures can be found reasonably easily; I've found endorsements for the use of a comma, a colon or no punctuation at all just before the opening inverted commas. The usual positioning of the closing comma or other stop etc tends to be country-specific, but both US and UK grammarians tend to favour a capital letter to start the quote. Of course, one should strive for accuracy with a quote, so arguably
The notice said: 'keep OFF the grass!!!!' might be required.