How much does the moon change in diameter as the gravity of the planets and sun act on it? What is the maximum distortion of the moon? Is it measured in centimetres  or metres or kilometres?
 A: The Moon has a "tidal bulge" of about 50 cm due to the Earth's gravity.  This was measured in 2014 via data from the Lunar Reconnaissance Orbiter.

[T]here is enough force to raise a bulge about 20 inches (51 centimeters) high on the near side of the moon and similar one on the far side.  The position of the bulge actually shifts a few inches over time. Although the same side of the moon constantly faces Earth, because of the tilt and shape of the moon’s orbit, the side facing Earth appears to wobble. From the moon’s viewpoint, Earth doesn’t sit motionless but moves around within a small patch of sky. The bulge responds to Earth’s movements like a dance partner, following wherever the lead goes.

For more information, see Marazico et al., "Detection of the lunar body tide by the Lunar Orbiter Laser Altimeter", Geophysical Research Letters 41 (7), 2282-2288 (2014).
The tidal effects from any other body in the solar system would be much smaller, since they fall off proportionally to the cube of the distance.   The tidal effects of the Sun on the Moon are about 0.6% the size of the Earth's effects on the Moon, and everything else in the solar system would have even less of an effect.
