No lease verbal agreement

I moved into my apartment on april 1st under a verbal agreement and was informed that a lease would be brought by later that week. We never received one. My wife and I payed 1 month rent and security deposit under the understanding that we would be there for a year. However now we are wanting to move due to problems with neighbors (second set since we moved in. They are getting evicted), apartment heat issues, (landlord supposed to fix), paint chipping in rooms (have children),  and me loosing my job. We have found a place that has lower rent since she will be the only one working until I locate another job. What type of notice do we need to give our landlord and can we get our security deposit back. The place was not cleaned when we moved in. However we are going to clean it before we leave.