ummm power steering
check your power steering fluid
ball joints or tie rods
soounds like steering wheel fluid needs to up
The most common cause for a squeaking noise when turning the steering wheel on any vehicle, including a 2001 Toyota Avalon, is the belt that runs the power steering pump. If the belt is fairly new, a small drop of any dish soap on the belt while the car is running will clear up the noise. If the belt is worn, it needs to be replaced.
could be the power steering belt, axle going bad. power steering pump it self could also be bad.
A bad bearing can cause can the front end of car to make a squeaking noise when turning steering wheel either direction. It can also be caused by bad suspension.
Most likely it is low power steering fluid. Check fluid and see if noise goes away.
squeaking noise coming from sleeve covered arm coming from steering column to the wheel
The problem is most likely a loose belt, this will happen when steering piston and pump is under a load as in turning. More torque is required to spin pulley.
try checking fluid level
ball joint or tierod end