Repository pattern in C# without Entity Framework

You don't need to make your repository IDisposable, and to use Task you should implement your entire class with the Async programming model. I have updated your code below which should get you close to a compiling baseline that you can then extend.

 // Removed the IDisposable interface
 public interface IDeliveryRepository
 {
     IEnumerable<Delivery> GetDeliveries();

     // Changed the below from a Task to a Delivery as the return type. To use Task, 
     // your entire implementation should be asynchronous.
     Delivery GetDelivery(int id);
     void Insert(Delivery delivery);
     void Delete(Delivery delivery);
     void Update(Delivery delivery);
 }

 public class DeliveryRepository: IDeliveryRepository
 {
     public Delivery GetDelivery(int id)
     {
         Delivery delivery = null;
         var sql = "SELECT d.id , o.owner_id, o.name FROM delivery d JOIN owner o on o.id = d.owner_id where id = :t";
         using (var con = new OracleConnection(AppConfig.CALL_CENTER_CONNECTION_STRING))
         {
             con.Open();
             using (var cmd = new OracleCommand(sql, con))
             {
                 cmd.BindByName = true;
                 cmd.Parameters.Add("t", id);
                 using (var oraReader = cmd.ExecuteReader())
                 {
                     while (oraReader.Read())
                     {
                         delivery = new Delivery
                         {
                             Id = oraReader.GetString(oraReader.GetOrdinal("id")),
                             Owner = new Owner
                                {
                                 Id = oraReader.GetString(oraReader.GetOrdinal("owner_id")),
                                 Name = oraReader.GetString(oraReader.GetOrdinal("name"))
                             }
                         };
                     }
                 }
             }
         }
         return delivery;
     }

   public void Insert(Delivery delivery)
   {
       /// Add your code here 
       throw new NotImplementedException();
   }


   public void Delete(Delivery delivery);
   {
       /// Add your code here 
       throw new NotImplementedException();
   }

   public void Update(Delivery delivery);
   {
       /// Add your code here 
       throw new NotImplementedException();
    }

    public IEnumerable<Delivery> GetDeliveries();
    {
       /// Add your code here 
       throw new NotImplementedException();
    }
}