Is it possible to tame and train wild songbirds?

Well you might be able to get them to eat out of your hand. If you sit very still in the same place every day eventually put bird seed in your hand. When they come, let them come to you. You can't teach them tricks, that's only with parrots and other kinds like that. You cannot domesticate a song bird, especially w/ out putting them in a cage. If you had them in a cage it would take many generations of the birds for them to even start to become docile. If you sit near a bird feeder they might come sit on your shoulder.