Usual John sends this in: “I get that Venus tried to say something off-color, presumably a play on “dangling participle,” but what was it? Based on the statement by El Jefe (the figure in armor, I believe a personification of the cartoonist), I take it that the remark may have been not safe for work.”
Comics I Don't Understand 
I think if his “participle” were long enough it probably would dangle.
Personally, I wouldn’t consider any of those to be puns. I don’t even get the “They order. They pay. They quaff” joke.
Three verbs, to remember what verbs are. Just like the one about the quotation marks has (air) quotation marks in it. Not really a pun or even a joke but using the joke structure to tie together a name and what it is.
Not sure what Venus’ joke was – something about it dangling into the bar (meaning piece of iron, rather than drinking spot)? That was my guess when I saw this originally.
Also, why is Shakespeare speaking in unmetrical rhymes?
Even worse, they’re sort of metrical (imperfect anapestic tetrameter), but like Dr. Seuss, not William Shakespeare (which is iambic pentameter, of course).
“Three verbs walk into a bar. They order. They pay. They quaff” could be an illusion to Julius Caesar’s famous “Veni, vidi, vici”. And the three verbs walking in are obviously order, pay, and quaff. I get it, but even as a lover of puns I don’t really care for this one.
She, um, she didn’t say anything. There isn’t necessarily a specific joke the author had in mind, and recall these are fictional characters who are not actually speaking. The phrase is suggestive enough that it doesn’t really need a punchline, so the author punted it.
(It’s also not funny at all. That’s a level of humor for children and drunks.)
Usual John has explained it. Sometimes, there is nothing more to ‘get’.
Not to mention, all those bloody, commas. What’s up, with them?
Yes, it has to be a juvenile joke about dangling a participle.