First, we must define "unstoppable" and "immovable." Hopefully, everyone knows what "force" and "object" mean.
unstoppable: impossible to stop
immovable: impossible to move
Newtonian physics: of or relating to the principles taught by Isaac Newton, including his 3 laws of motion; the forces that act on normal matter. (Leave quantum and antimatter out of this.)
Pretty simple, but we'll make it clear so that no one can twist the meaning.
First of all, I would like to establish that movement and position are relative. As Einstein stated, a box on earth with the force of gravity pulling objects "down" at 9.81 m/s^2 is indistinguishable from a box accelerating through space at 9.81m/s^2 to a person inside the box. This has to do with the law of inertia.
Now, in a similar situation, a person sitting in a train will appear motionless to someone else on the train but will appear to be moving at the speed of the train from the relative perspective of someone who is not on the train. Furthermore, someone with a really good telescope in space would observe the person moving at the combined velocities of the train, the rotation of the earth, and the orbit of the earth. Someone from outside the galaxy, if they could somehow see that person, would see that person moving at all of the above velocities combined along with the rotation of the galaxy and the movement of the galaxy away from the Big Bang.
All of these perspectives on that person's movement is relative, but it is undoubtable that that person was moving in relation to other objects.
Now, let us suppose that there was a stationary object immune to the influences of gravity, magnetism, or any other force. (This is impossible. Everything is influenced by some force or another. Even non-objects like light are affected by gravity. So I could stop here and call it a day, but let us suppose.)
Such an object is not immovable. It is made of atoms, which require the movement of electrons and such. This alone proves that the object can move, and thus, is not immovable. I could also stop here, completely correct.
Now, let us suppose that this object is somehow not made of atoms, despite the additional impossibility.
I remind you that motion and position are relative. If this object doesn't move, then from a moving object I will perceive it as moving in relation to me. From an objective viewpoint, my movement and its being stationary is indistinguishable from it moving and my being stationary.
"Now, K_Michael," RM might say, "but the position of the object is the same, so it hasn't moved."
That is untrue. Position and movement or lack thereof can only be seen in relation to other objects. Therefore, the only way to objectively perceive an object as unmoving is if everything else is unmoving. Since we know that other objects are moving, it is impossible for an object to be unmoving. There is no such thing as an immovable object.
For every action, there is an equal and opposite reaction.
This is a fundamental part of Newtonian physics. In other words, if there is an unstoppable force, there is an equally unstoppable force created simultaneously. This opposite force can, by merit of being an equal force, STOP the "unstoppable" force.
I bet you thought the second one would be equally long.