WebAPI No action was found on the controller

This is because there is a parameter name mismatch. From your route the value 1 is assigned to parameter named id and your action is looking for parameter named moduleId.

First option is to change your route like this:

config.Routes.MapHttpRoute(
    name: "DefaultApi",
    routeTemplate: "api/{controller}/{action}/{moduleId}",
    defaults: new { moduleId = RouteParameter.Optional }
);

Second is to change your URL like this:

http://localhost:37331/api/action/FindByModule?moduleId=1

So the parameter name match.