It's rather hard to know.
Much like films and comics routinely have people who would be speaking a foreign language speaking English (or whatever language) for the benefit of the viewers, it's very probable that what we see in Black Library books - or GW publications in general - is a similar "translation".
These characters almost certainly don't speak English, or anything that bears resemblance. Consider how far language has developed in a few hundred years - a moderner would seriously struggle to get through Middle English (particularly the early variants), and that's less than a thousands years old. Indeed, Early Modern English (think Shakespeare) is work for many moderners to make out.
As an example, "Wherefore art thou Romeo" does not mean "Where are you, Romeo?" as many seem to think - wherefore means "Why". So, the sentence as a whole is therefore a question about why he had to be of a family she couldn't marry.
Now multiply these changes by the linguistic needs of a million worlds and nearly forty thousand years. Obviously, we'll not end up with anything that resembles modern languages at the end of it. (And this leads to some of the odd linguistic jokes I've made in "After Hours".)
This goes for Low Gothic, High Gothic... any of it really. However, from the perspective of what we actually see...
Low Gothic tends to be represented by English, or dialects of it. It's occasionally mixed with words or phrases from other languages, depending on what "country" the character's planet is supposed to be loosely based on.
High Gothic tends to be represented by Dog Latin (although if/when I'm writing it, I do my best to make it honest Latin.)
Lingua-Technis... not really sure. Probably any language you'd use for speaking to or about machines. Could be binary or assembler code for talking to them, and about them... well, anything. Likely a catch all term.
Local: Just like the languages of our word differ from English in so many ways, this can be represented by anything. Personally, I tend to work on the basis that most planets have a language (or languages) of their own, and that many people in the Imperium are bilingual for at least the local dialect of Low Gothic and their own planet/country's language. Which of Low Gothic or the local language is dominant will vary.
Slang: Whatever the hell you want.