Robust control of mechanical systems with multiple uncertainties remains a fundamental challenge, particularly when nonlinear dynamics and operating-condition variations are intricately intertwined. Although deep reinforcement learning (DRL) combined with domain randomization has shown promise in mitigating the sim-to-real gap, simultaneously handling all the sources of uncertainty often leads to sub-optimal policies and poor learning efficiency. This study formulates a new curriculum-based continual learning framework for robust control problems involving nonlinear dynamical systems in which multiple sources of uncertainty are simultaneously superimposed. The key idea is to decompose a complex control problem with multiple uncertainties into a sequence of continual learning tasks, in which the strategies for handling each uncertainty are acquired sequentially. The original system is extended into a finite set of plants whose dynamic uncertainties are gradually expanded and diversified as learning progresses. The policy is stably updated across the entire plant sets associated with tasks defined by different uncertainty configurations without catastrophic forgetting. To ensure high learning efficiency, we jointly incorporate a model-based controller (MBC), which guarantees a shared baseline performance across the plant sets, into the learning process in order to accelerate the convergence. This residual learning scheme facilitates task-specific optimization of the DRL agent for each uncertainty, thereby enhancing sample efficiency. Finally, this study adopts the proposed method to design an active vibration controller for automotive powertrains as a practical industrial application. We verify that the resulting controller is robust against structural nonlinearities and dynamic variations; thus, it can realize successful sim-to-real transfer.