I have made a override to method Details in Nop.Web.Controllers.OrderController, but when I use DependencyRegistrar, to use my CustomOrderController it just ignores it.
In your case, no need to override action method. Rather at first delete OrderDetails route of Nop.Web project from your plugin route provider and add another route with url format orderdetails/{orderId:min(0)}. So whenever customer hit this url, your plugin controller action will be executed.
