Local perturbations in complex oxides, such as domain walls(1,2), strain(3,4) and defects(5,6), are of interest because they can modify the conduction or the dielectric and magnetic response, and can even promote phase transitions. Here, we show that the interaction between different types of local perturbations in oxide thin films is an additional source of functionality. Taking SrMnO3 as a model system, we use nonlinear optics to verify the theoretical prediction that strain induces a polar phase, and apply density functional theory to show that strain simultaneously increases the concentration of oxygen vacancies. These vacancies couple to the polar domain walls, where they establish an electrostatic barrier to electron migration. The result is a state with locally structured room-temperature conductivity consisting of conducting nanosized polar domains encased by insulating domain boundaries, which we resolve using scanning probe microscopy. Our 'nanocapacitor' domains can be individually charged, suggesting stable capacitance nanobits with a potential for information storage technology.