@Html.DropDownListFor(model => model.AdresId, (SelectList)ViewData["Adres"])
                <input name="action" type="submit" value="Новый" />
...
                @Html.DropDownListFor(model => model.ContactID, (SelectList)ViewData["Contact"])
                <input name="action" type="submit" value="Добавить" />

           switch (action)
            {
                case "Отправить":
                    Session["Order"] = order;
                    return RedirectToAction("Save");
                case "Новый":
...
                    break;
                case "Добавить":
...
                    break;
            }