> He called her, emailed her, texted her, tweeted her—all to no use.
Strictly speaking, I would need to write *texted her **and** tweeted her*, but I'm omitting *and* to convey a rhythm and sense of urgency. What do you call this kind of construction, and is it accepted grammar (at least for creative writing, if not in an academic context)?
That is called an asyndeton (the omission of a conjunction) and is perfectly acceptable in creative writing. It's the type of thing literature teachers love to look way too deep into in classic literature; I'm sure it will do well in a work of your own.