Historical linguists can do amazing things with oral language that I can't begin to understand how it's even possible, just marvel at the results. But I can talk a little about ways we can see in literature some developments that probably reflected spoken language.

Like one I have just come across in Middle High German, the language spoken (in various dialect forms) across much of the southern Holy Roman Empire in the later Middle Ages. "Schlepsack" refers to a sack carried by day laborers, especially fishermen, to haul their catch around. We have a couple of sources, however, that apply a second, colloquial meaning: adulterer. You can pretty much tell that a meaning like that evolved out of people's everyday use of it, rather than an author getting inventive.

Or take Shakespeare. Much Ado About Nothing is not much ado about nothing, it is much ado about genitalia. "Get thee to a nunnery" doesn't refer to chaste nuns, if you take my meaning.

It's probably harder to extrapolate from abbreviations and acronyms whether people were talking like that or just writing, because written shorthand was so common before print (and those abbreviations continued into the era of early print).

I will say that one thing I'm extremely curious about whether people said the acronym aloud is EFG/SFG in Middle German. It's "euer furstliche gnad"/"sein furstliche gnad"--Your Princely Grade/His Princely Grace. It is THE common shorthand to refer to people of that rank in the early 16th century sources I read. It wouldn't surprise me at all if people spoke those initials, but obviously I can't prove it.

Another thing people did in the Middle Ages was blend languages! Although real knowledge of Latin was very rare, most Christians would have picked up a bit of it hearing the liturgy in Church every week. So you get poets who will throw in random Latin words at the end of a line in German or French or whatever to make the rhyming couplet and meter work. That too seems like a thing people would do in everyday speaking.

Arguably, the entire development of the western European Romance vernaculars out of Latin reflects spoken slang, as would Middle English's union of Anglo-Saxon/Germanic, straight-up Latin, and Norman influence. Classical Latin itself was a formal written language; people spoke many many variations on it we call Vulgar Latin. (/u/XenophonTheAthenian is our resident expert; this thread has some great discussion).

Are you asking about spoken language in particular or are you interested in abbreviations in writing, too? I'm not much of an expert on the former is why I'm asking (others here are, though).