Ham is your basic antagonist, in that he actively tries to antagonize people. He's a meanie. He picks on Julian because he's different; he picks on Mrs. Olinski because she's weak (at first); he tries to drug Ginger because he refuses to play by the rules. But none of his misdeeds end up sticking, and in the end he just sort of fades out. As Mrs. Olinski and The Souls get stronger, he doesn't have the courage to face up to them.
It fact, it's almost as though the real antagonists here are the other selves of The Souls—the selves that want to stay hidden in their shells, or hang on to their red wagons, or let Arnold eat the poisoned treats, or refuse to save the baby turtles.