In "The Raven," by Edgar Allan Poe, is the raven really talking to the narrator or is the narrator just imagining the raven talking to him?

The short answer is
that we can't know for sure.  The narrator's first thought about the raven's speech seems
entirely plausible: he assumes that the raven's one word "is its only stock and store /
Caught from some unhappy master" who clearly had a difficult life and, therefore, spoke the
word quite often (lines 62-63).  The narrator believes that the bird learned the word
"nevermore" from hearing his master say it again and again.  This could be
true.

It could also be true that the raven isn't actually speaking at all,
that its cawing croaks...