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While throwing heavy objects at earth would be an effective strategy, Earth is large. We also have an atmosphere that would burn off some energy from projectiles. An object moving at 10% of light speed would be farily bright. The solar system isn't empty and hitting gas particles at 10% of light speed causes a sizeable bang. Meanwhile we have a whole planet full of capacity to lob stuff toward the enemy.
As for changing orbits it requires energy. Slowing down from those high speeds would require extreme energy and a large part of the enemy ship would consist of fuel and material for the rocket used to slow them down. Accelerating the ship in other directions to preform evasive maneuvers would consume additional fuel. Space ships don't fly like fighter jets. There is a reason why rockets are giant gas tanks with a tiny capsule on top.
With that said it would depend on our ability to fight back with a sizeable force, the efficiency of their engines, the size of their force and the capacity of their counter measures. We would be at a technological disadvantage.
We are not the first people to think about this topic. I've read lots of hard sci Fi, and they all agree planetary defense is near impossible.
Dodging objects is the only real defense in space battles. Even if you can spot an object it does not mean you can impart enough energy on that object to stop it in time.
If a spaceship is past Jupiter it's about one light hour away. At that distance a 1mph change in a direction means they can dodge a laser by a mile. Lasers aren't particularly effective, but they are the fastest weapon, so if you can't hit something with a laser you can't hit it with a bullet. A 1mph change in velocity is nothing for something capable of crossing interstellar distances.
But all of that is moot. If you can cross interstellar distances you can probably calculate orbital mechanics. The earth has a predictable path through space. There is no need to even enter the solar system. They could lob objects at us from light years away. And they don't have to follow the orbital plane where all the convenient gas and dust is. The north and south pole are valid targets for an object with enough mass or speed.
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