Using colored paper or sheets of foam rubber Foamies,
cut out the parts below and hot glue them together.

Faces

Generally, the bigger your head relative to the body,
the more expressive your critter will be.

Body Shapes

You can save valuable materials and cut more accurately
if you cut a small rectangle from the corner of a sheet.
Then cut the body part from the small rectangle.

Wings

You could add feathers and colorful beads.

Feet

Try looking in your Premium Quality Junk  box for
stuff that could be used as body parts.

If you think you're a hot shot inventor,
try hot gluing the pieces together
so the cuckoo has a 3 dimensional quality.
You could glue pipe cleaners between the foam
rubber pieces. Then you would have flexible
joints and could put your wild thing in
many different positions.

Now you need to build a contraption on
your door to make the cuckoo fly.

Solution #1

Put a screw eye in the ceiling or middle of a door frame
and another one on the side of an entrance.

Cut a piece of nylon string about 10 feet long.
Heavy fish line is good.
Thread the string through both screw eyes.

Attach the string that hangs from the
center of the entrance to your Wild Thing. 

Attach the string on the side of the entrance
to a hole in the rear wheel of your
remote control chassis.

Put screws through the wood platform on the
RC chassis into the side of your door frame.

Use the remote control to turn on the chassis
which will make your Wild Thing circle when
the string gets wound.

Solution #2

Another option is to build a hand crank
out of wood and a coat hanger wire.
Tie the string to the loop at the end of the coat hanger.
When you turn the crank, eventually the string will
make your bird fly around.