Eastbound, without the S is used like: I'm Eastbound on Route 10. I guess it's used almost as a noun. Eastwards is an adjective. As in "they are headed eastward". Neither of these expressions are used very often. Much more common to say "I'm headed or travelling east" That's not a great answer, sorry about that. We don't use it very often. Hope everything is well with you in Ukraine!

I think eastbound is direction with movement. "he is driving eastbound" Eastward/s is direction with or without movement " he is looking/driving eastward/s"

I agree with Brian. If you look up BOUND, used in this way, it means ON THE WAY TO.