With advancements in deep learning, neural simulators have become increasingly important for improving the efficiency and effectiveness of simulating complex dynamical systems in various scientific and technological fields. This paper presents a novel neural simulator called Context-informed Polymorphic Neural ODE Processes (CoPoNDP), aimed at addressing the challenges of modeling dynamical systems encountering concurrent environmental and temporal distribution shifts, which are common in real-world scenarios. CoPoNDP employs a context-driven neural stochastic process governed by a combination of basic differential equations in a time-sensitive manner to adaptively modulate the evolution of system states. This allows for flexible adaptation to changing temporal dynamics and generalization across different environments. Extensive experiments conducted on dynamical systems from ecology, chemistry, physics, and energy demonstrate that by effectively utilizing contextual information, CoPoNDP outperforms the state-of-the-art models in handling joint distribution shifts. It also shows robustness in sparse and noisy settings, making it a promising approach for modeling dynamical systems in complex real-world applications.