When oiled, the mechanics are fairly silent. What usually makes noise in robots like this are the stepping of the stepper motors.
Using microstepping helps a lot, but I went further.
I use dither stepping, where microstepping and digital
signal processing are combined directly with cybernetics
to give smooth silent movement to the robot.
In the beginning I used microstepper controllers, but they have
been replaced with H-bridges driving the stepper motors
directly. They are controlled by an Atmel microcontroller which
in the background runs my interrupt based driver routine. It
uses negative positional feedback with smooth bessel filters
implemented as coupled differential equations.
(The mechanics make some small noise when moved very fast.)