Can their smallest unit, which btw, not sure what dimensions it is ?
Yes, there is a large assortment of "small" µController boards, not all necessarily Arduino. To some extent size is predicated on what features you might need. Possibly bluetooth etc
Can it be placed in a small plastic object?
Yes. But in my mind the answer is so obvious that I feel I'm not getting the essence of your question.
The main features I'd want to have is for the arduino to sense when the object is moving. ie when the arduino unit ITSELF is moving. Is there a recommended motion best for that?
I'd want to do certain things once it stops moving as well.
An accelerometer will provide acceleration but not movement. So you will have to be more specific of your goal.