I know this is old and I am not sure if you are still on here but this can be a problem with hearing. Number one sign is that he doesnt respond to your voice. Even infants that do not comprehend words can read the tone in a persons voice. I test hearing and a moody child that was slow to speak is the first sign I look for.
Sounds like a normal 3 year old to me. He may be more active, some children just are. It is good that he gets his moods out instead of bottling them up inside (those are the kids I worry about, the extreme quiet ones). If a child feels safe in his environment, then he will be comfortable enough to act out when upset. Also, if he is picking up on you and your husband being irritated, he will act out more. You need to be calm and happy.