if you have the talk to animals skill, you can start a conversation with a rat and while it is conversing with you (ie, not moving) you can easily kill it with any of your other characters.
I find rats hard as hell to click on. I certainly fail 9/10 times when they are in motion. I have to wait for them to run to a corner, then spin my camera around to see them, and even then sometimes there is no camera angle that will let me click them. So I have to walk towards them so they run again, and hope they go somewhere my camera will let me click on them.
