I have found a much longer version (many verses added later) which makes it clear that in all of the third verse the bird is speaking. Wilfried's idea ( "tröst mich Waldvögelein" (apposition to me): console me, the birdi) is the correct one.

The first two translations have been incorrect here (BTW, I had made the same mistake when reading it). "Me" in the third line of verse 3 refers to the bird.

Wolfgang