The stealing and breaking could also be stemming from how often he's had everything he's known torn out from under him (attachment issues). That's a lot to deal with in just a few years of life, and if you look at it, he's been through that 1/3 of his life, so it's something he's come to expect.
Has he had any treatment for Fetal Alcohol Syndrome (FAS)? Been seen for attachment issues, in addition to autism? These kids also do what they see, so what did he see before he came to you?
I also suggest you pick up The Explosive Child, it's a great book, and while you may not use everything in it, it will help you get a better look in his mind, and give you that pause to consider where he's coming from before you react to him. After a while you'll get better at seeing when he's working up to this behavior and can start making the trial/error moves to head it off.
Is he in mainstream school? Does he have an IEP or are you working towards getting him one?