One of the best ways to advertise your business is to put yourself in the position of your customers. In other words, if you were looking for a moving company, where would you look? And who would look the most often?
My suggestion is to locate several large apartment complexes near your business. You can inexpensively put together some flyers with tear off strips with your phone number on them. Put them up on the bulletin boards in the laundry rooms, community areas, or see if you can't partner with the apartment managers by showing them you have a reasonably priced service and are conscientious of their property. You might offer them a finders fee too. I would look for complexes with middle aged to elderly renters - folks who appreciate good work because they can't do it themselves. And once people see your trucks in the complexes frequently, they will call you first.
You might expand your business by not just moving whole homes, but to deliver and install new/used furniture, to re-arrange items in a home, or to move furniture before carpet is installed. I'd target the same people as above, but here you could post flyers single family home neighborhoods so they could also use your services. With so many retirees moving to Oregon these days, I know I've had to try to find this very service for older adults in my community. Unfortunately there aren't any such services I've found down on the south coast.