A cost-effective deep transfer learning (TL) learned with characteristics derived from the constellation diagram is proposed for executing modulation classification and optical signal-to-noise ratio (OSNR) estimation for the future generation of elastic optical networks. The information acquired with the ImageNet dataset is transferred using pre-trained TL versions including VGG19, ResNet152V2, InceptionV3, and ResNet50 to identify various modulation formats and their corresponding OSNR. Adam optimizer is employed to ascertain the appropriate settings for the hyperparameters. Numerical results demonstrate that the proposed VGG19 method achieves the highest level of accuracy (100%) in the recognition of various modulation forms. To fulfill the requirements of actual use, OSNR monitoring is also explored, with a total precision equal to 95.2%. Furthermore, a thorough investigation of the impact of training data dimensions, on TL performance is conducted. The outcomes of the proposed method demonstrate that the suggested TL-based algorithms are more accurate and need much less training and testing time than non-TL approaches.