Roadmaster Chromium Edition rear wheel falls off
As @ Daniel R Hicks has suggested you need the proper hardware. From the photo it appears you have conventional/automotive nuts. You need flanged nuts or oversized washers with a serrated face or both. The oversized washers are thicker and have a larger overall diameter but the correct size hole for the axle.The dropout is the slotted section of the frame that the axle slides into. You may have an issue with the condition of the dropouts. If the rust has pitted the frame enough, the hardware may be biting into the high spots resulting in insufficient grip by the nut. Clean the clamping area with some emery cloth, wire brush or a file then clamp the nut tight. The Park Tool BlueBook has a torque value of 22-33 footpounds as a guideline. To give you a comparison that is about 1/3 of what you would tighten a cars lugnut.