I was recently reading through some old Greek literature and was wondering how much of the content of these plays the average Athenian could understand/comprehend. The plays of Sophocles for example, seem to me relatively high brow even by modern standards.
I'd also be interested to know how Homer's epic poems were experienced, given how long it is (my audio book was almost a dozen hours) and the necessity of a trained bard to be able to hear it.
While Athenian tragedies often used deliberately archaising language (in layman's terms, trying to sound old-timey), they were written to win public competitions, and so they could not be too high-brow or elitist. They had to be understandable and relatable to the audience and the judges. If they sound artificial, it is probably because they were works of poetry rather than prose, meant to follow a specific meter (the rhythm of long and short, stressed and unstressed syllables) and usually intended to evoke a mythical world.
It's possible that the impression you got of particularly high-brow language was a result of the translation. Some common translations of ancient Greek texts are themselves a century old or more. If they also try to replicate the original text's archaising tone, the distance between the English text and a modern reader can feel very great.
Given the length of the Homeric epics, it's pretty clear that they would not be performed in one sitting. Rather, trained storytellers (called rhapsodes) would perform chunks of it, with the selection presumably depending on the wishes of their patrons. The occasion would be, again, public competitions, but also more private drinking parties of the leisure class, in which wealthy hosts could give a good impression by providing guests with the quality entertainment offered by a rhapsode.