To learn the opposite of west, it helps to visit the compass rose at the middle of the map, plus the North, South, and East poles. The East Pole and the compass rose are pretty easy to find.
To reach the South Pole, first head north to the Cave of Yesterdays and grab that key. Go east, the south, then south, to the big door. Unlock it with your key, and go south to the South Pole.
To reach the North Pole, first head south to the mines and grab that shovel. Go east, then east, then north, then north, to the graveyard. Dig up the grave of the Hornet King. Take him south, then south again, so he can usurp the Hornet Vizier, who was a hornet all along! This is how you learn that screaming incapacitates robots.
Start over. Head north, north, and east to the mountain pass. Scream to incapacitate its robotic guardian. Go north to reach the North Pole.
From the three Great Birds, plus the compass rose, we know that the opposite of east is four letters long, starts with T, ends with G, and comes from trees. It must be TWIG. Go twig from the beginning to reach the Twig Pole, where the Great Bird of the Twig will confirm that your journey is at an end.