Generally, for older Dodge 360 engines (pre-1990s), a 10W-30 or 20W-40 oil is commonly recommended, especially in warmer climates. 20W-40 offers better protection at higher temperatures. In colder climates, 10W-30 might be preferred for easier starting.
For newer models, or if you have the owner's manual, refer to that manual for the specific viscosity recommendation. The manual will take into account the engine's tolerances and operating conditions. It might even suggest a different weight depending on the season.
Always use oil that meets or exceeds the specifications listed in your owner's manual. Using the wrong viscosity can lead to poor engine performance and damage.