In multi-sequence Magnetic Resonance Imaging (MRI), the accurate segmentation of the kidney and tumor based on traditional supervised methods typically necessitates detailed annotation for each sequence, which is both time-consuming and labor-intensive. Unsupervised Domain Adaptation (UDA) methods can effectively mitigate inter-domain differences by aligning cross-modal features, thereby reducing the annotation burden. However, most existing UDA methods are limited to one-to-one domain adaptation, which tends to be inefficient and resource-intensive when faced with multi-target domain transfer tasks. To address this challenge, we propose a novel and efficient One-to-Multiple Progressive Style Transfer Unsupervised Domain-Adaptive (PSTUDA) framework for kidney and tumor segmentation in multi-sequence MRI. Specifically, we develop a multi-level style dictionary to explicitly store the style information of each target domain at various stages, which alleviates the burden of a single generator in a multi-target transfer task and enables effective decoupling of content and style. Concurrently, we employ multiple cascading style fusion modules that utilize point-wise instance normalization to progressively recombine content and style features, which enhances cross-modal alignment and structural consistency. Experiments conducted on the private MSKT and public KiTS19 datasets demonstrate the superiority of the proposed PSTUDA over comparative methods in multi-sequence kidney and tumor segmentation. The average Dice Similarity Coefficients are increased by at least 1.8% and 3.9%, respectively. Impressively, our PSTUDA not only significantly reduces the floating-point computation by approximately 72% but also reduces the number of model parameters by about 50%, bringing higher efficiency and feasibility to practical clinical applications.