If I were to follow the path of English through time, how far back would I have to go until my speech seems...peculiar to others? Until it gets noticeably awkward between I and another speaker? Until it becomes difficult to understand each other? Until the discussion is intelligible?

Hi there. You might be interested in this thread:

What is the furthest year I can go back in time to England and be able to communicate with people?

Probably some time in the early 1500s, though the late 1400s might be possible with some patience and concentration. There might be some head-scratching over pronunciation, multiple meanings, and figures of speech but you'd be able to recognize what you heard as English.

He then provides three readings from Beowulf (Old English, from the Anglo-Saxon period), The Canterbury Tales (Middle English, from the late Middle Ages), and one of Shakespeare's plays (Early Modern English, from the Tudor era).