What is the Sun's gravitational pull strength?
The strength of the Sun's gravitational field depends on the distance from the Sun.
The Sun, and any other body, has a gravitational field. This field causes any other body to accelerate. Newton described this with his inverse square law and his second law force
This says that the acceleration
General Relativity (GR) redefines gravity. It is not a force, it is a consequence of space time being curved by mass, energy and momentum. For relatively small masses, which includes the Sun, and low speeds GR reduces to Newton's laws.
Everything in a gravitational field experiences an acceleration towards the centre of the body causing the gravitational field. Everything follows a geodesic, which is the 4 dimensional equivalent of a straight line in curved space time.
So, the Sun doesn't exert a pull strength, it simply bends space time because of its mass and motion.