A multi-parameter estimation scheme for optical fiber link is proposed using deep learning (DL) technique. Instead of using a single model for multi-parameter estimation, a cascaded neural network architecture comprised of convolutional neural networks (CNN) is proposed, where the predicted value for each stage becomes an input parameter for the next stage. The proposed cascaded structure is employed for modulation format identification (MFI), optical signal-to-noise ratio (OSNR) estimation, and fibre link length estimation, in the same order. The input dataset used in this work consists of in-phase and quadrature (I/Q) currents as obtained from coherent detection. The proposed scheme needs no prior pre-processing steps, and the model can be deployed directly in the optical fiber transmission system. The OSNR and fibre link length estimation are treated as regression tasks, whereas MFI is treated as a classification task in our proposed cascaded model. The model attains 100% accuracy for MFI. Moreover, the mean absolute error (MAE) stands at 0.3246 dB for OSNR and 0.1140 km for fibre link length estimation. The model is also tested against intermediate values for fibre link lengths, which were not used during training. The MFI accuracy obtained for this case is 99.95% for QPSK and 100% for all other modulation schemes under consideration. The OSNR estimation has an MAE of 0.8945 dB, and the fibre link length estimation has an MAE of 0.854 km for the unseen values.