Landlord wants us to stay another month when we already have another place?

We recently got a new apartment and made plans to move out the end of the month before the new month kicks in and the new rent is due. Hubby went to tell our landlord about it and our landlord told him we are not allowed to move out until the end of next month. Normally, that would be a given in any other situation. However, we do not have a lease, he's not losing money because we aren't moving in the middle of a month we are moving at the end, and on top of that he's a real crappy landlord. When something needs fixed, we call and he never calls us back or even comes over to fix it. We have to fix it and he doesn't reimburse us for it. He's supposed to mow the gr but he doesn't do that. The other neighbor does it and he doesn't reimburse him for the gas for that either. Therefore, I don't think we owe him more than a 3 weeks notice. Which is what we gave him. He said if we move before the end of next month, he's keeping our security deposit. Hubby said to just keep it for the rent then and he said we would not only NOT get the deposit back but we would still owe for the month of August when we aren't going to be living there. I'm not sure what to do. Now we will be paying bills and possibly rent at two places. Thankfully our new landlord said we didn't have to pay the first months rent until we are actually moved into the place and that we can use this time to get painting done and shampoo the carpets but the fact that the old landlord is being so pissy about us moving is ridiculous. with no lease and him not fixing things or reimbursing things, I don't think we owe him anything. Even if we did have a lease I would imagine since he doesn't fix things here like a landlord should that the lease would be void right? Is there anything I can do or are we pretty much stuck living in this dump for as long as he makes us?