Does the earth spin on its axis only?

Answer 1

If by spin you mean "rotate daily" then yes. But you could refer to our "orbit" as a spin around the sun. But if you want to refer to "spin" as any oscillatory/periodic motion of the earth, then we spin around our central axis, we orbit around the sun, we precess the rotational axis around a precession axis, our obliquity oscillates periodically and our eccentricity oscillates around the foci of our elliptic orbit which is near the center of the sun.

These characteristics of our orbit are known as the Milankovic cycles.