When you say 'hurting animals', I am going to assume you are implying he gets too rough with them. Not piercing their ears or pulling out whiskers, which obviously would be a sign that a medical professional needs to get involved for further diagnosis.
I think you have a simple case of a bored little boy who is testing his boudaries as well as cause/effect reactions amongst his peers and pets. "Hmm, math sure is boring today. Wonder how little Suzie will react if I pull her pony tail? Gosh, I got yelled at, but gee whiz that sure was funny how she screamed!"
It also sounds like he's seeing how far he can push his little brothers before they cry uncle or he gets in trouble. Trust me as the youngest child that this was common. Also may be looking for that attention he sees the younger children hogging. Negative attention is better than no attention at all!
Nothing you've listed sounds malicious. Perhaps a little more positive attention, positive attention when he's had a green light day, and a quick, wordless re-direction to a time out spot when he exihibits the negative behaviors may be all it takes to get him refocused.
(The dog/cat will use their own methods to let him know what he is doing isn't ok. Some of my children's first sentences were "First she growls, THEN she bites!" They learned very quickly that there was only so far you could shove your fingers in a dog's ears and mouth before the dog would let you know it is NOT ok. :))
Good luck momma!