Current mainstream research in multivariate time series (MTS) forecasting often assumes that all data are static. However, real-world MTS data typically arrives continuously in a streaming manner, which we refer to as streaming MTS. The statistical characteristics and spatiotemporal graph topology of these data evolve over time, presenting two key challenges: the model's ability to adapt to new data distributions and the enhancement of cross-domain generalization capabilities. In this paper, we propose a streaming MTS prediction framework. We begin by designing a lightweight spatiotemporal causal learning model that captures generalizable causal spatiotemporal features from a decoupling perspective. Next, we introduce a framework to enhance the model's streaming learning capability, leveraging the adaptability of continual learning while strengthening cross-domain representation abilities. Specifically, we reformulate continual learning as a multi-task learning problem and present a multi-task optimization algorithm that identifies a set of Pareto-optimal solutions to address the inherent stability-plasticity dilemma in continual learning. Finally, we propose a topology-aware feature propagation strategy that disseminates well-trained node embedding features to unseen graph structures, thereby improving the model's cross-domain generalization. Results on real-world datasets demonstrate that our model achieves superior forecasting performance while substantially improving computational efficiency and memory usage.