There's no "keep sorted automatically" option. In a sequential project, the order in which you do the actions matters, and the proper sequence is not necessarily determinable from looking at the due dates. OmniFocus gives you the tools to put your actions in the desired order, and if you add additional ones, you can repeat the process, or simply insert the new item(s) in the appropriate spot. If you have an action selected when you click the Add Action button, the new action will be inserted immediately after the selected action. If you do the same but instead press the return key, you'll get a new action immediately after the selected action, and if you want it before the selected action, holding down the shift key while pressing the return key will insert the new action immediately before the selected action.
If you just want to have lists of actions, don't care about sequences, and want to see what is due when, go over to context mode view (command-2) and there the view bar sorting works on a per-action basis. Group and sort your actions by due date and you'll see an ordered list across all of your stuff.