According to Astronomy.com, the Sun is nearly spherical with a very slight equatorial bulge, Earth is an oblate spheroid, and the Moon is somewhat lemon-shaped. These three bodies' shapes are influenced almost entirely by their gravity and centrifugal forces acting on them.
The Sun is the most nearly spherical-shaped body in the solar system. The difference in its equatorial and polar circumference measurements varies by only one part in 17 million. Earth is also very round, owing to its strong gravity. It is not, however, a perfect sphere. Earth's rotation causes it to bulge somewhat at the equator and flatten at the poles. The Moon is both smaller and less dense than Earth, and therefore its gravity is less able to pull it into a perfect sphere. The strong tug it feels from Earth has not only tidally locked the moon into always showing the same face to Earth, but it has also stretched the Moon very slightly into an oblong shape.