Accurate forecasting of the Indian Ocean Dipole (IOD) and El-Niño-Southern Oscillation (NINO3.4) is crucial for understanding regional weather patterns in the Indian subcontinent. Addressing the challenges associated with IOD and NINO3.4 prediction, a robust multitask autoregressive deep learning (DL) model is introduced for precise forecasting of these indices and key grid projections sea surface temperature (SST), surface-level pressure gradient (SLG), and horizontal wind velocity (U-Comp) over a short to mid-term window (20 months). Utilizing spatiotemporal (SST, SLG, U-Comp) and temporal (IOD and NINO3.4) modalities, the proposed model predicts future IOD and NINO3.4, as well as SST, SLG, and U-Comp, in an autoregressive scheme. The multitask learning component regularizes the model, effectively capturing the evolving dynamics of global patterns conditioned on IOD and NINO3.4. The comprehensive evaluation explores various task settings, including a duo-setting that predicts IOD or NINO3.4 with spatiotemporal information, showcasing notable proficiency. In a multitask environment, where both temporal IOD, NINO3.4, and spatiotemporal SST, SLG, U-Comp are predicted, the model successfully forecasts IOD and NINO3.4 indices alongside grid projections with modest accuracy in root mean square error (RMSE). To enhance the model's interpretability regarding spatiotemporal dynamics, a tailored version of Grad-CAM is employed, providing critical insights for climate prediction. This research advances climate prediction models, offering a comprehensive framework with significant implications for informed decision-making in the Indian subcontinent's climatic context.