Those three sound completely different to me, as far as how I’ve been pronouncing them goes. “Their” doesn’t have the extra lagging e sound (as in the e in err) in “there” where I curl my tongue upward at the end. “They’re” preserves the ey sound in “they”, just concatenated with an r as in err sound.

When I say, “They’re there,” people can make out what I’m saying, though as more people seem to tell me that these are just homophones, maybe they’ve just been relying on context.