I remember seeing a cartoon or anime movie when I was little(maybe six or seven) about a young woman who was cursed to look and feel like an old woman. She discovers a walking house in her travels as an elder. The inhabitant of the house is seen in a dream as a demon bird/man fleeing down a dark tunnel. I can't remember the name of the movie.
That could be Howl's moving castle, which has a girl transformed into an old woman, a walking castle, and a man turning into a bird monster. It came out in 2004.