Remember things were a lot quieter in general in the 1840's (he types over the roar of his computer cooling fan). No motorized traffic, no fans, no flourescent light hum, etc. This means that not only could folks hear better, they probably had better hearing too, their ears not having had to deal with a constant assault of background noise all their lives. But as far as 3000 people hearing a banjo contest, I'll bet that any large symphony hall could hold that many and they'd all be able to hear an unamplified banjo just fine.

Back to megaphones: they are still used by many cheerleading squads. I bet your local high school has a catalog where you could order one, if you don't want to try making one from cardboard and shellac.