Marine oil spill monitoring plays a critical role in environmental protection and emergency response. Synthetic aperture radar (SAR) provides all-day, all-weather, and wide-area imaging capabilities and has become a primary sensor for operational oil spill surveillance. Nevertheless, SAR oil spill segmentation remains challenging. Real slicks are easily confused with look-alike dark formations; oil film boundaries are weak and fragmented under speckle noise; and small and sparse targets, such as ships, are easily overlooked amid the dominant sea surface background and complex coastal structures. To address these challenges, this paper proposes SDE-Net, an encoder–decoder network built on a ConvNeXtV2-Tiny backbone and a UPerNet-style decoder with three task-oriented modules. The Strip-Directional Local Enhancement (SDLE) module refines elongated low-contrast cues in the shallow lateral features of $C_2$ and $C_3$ while limiting the indiscriminate enhancement of speckle-contaminated responses. The Dynamic Scale Pyramid Context (DSPC) module redesigns pyramid-based context aggregation at the deepest stage by introducing an input-conditioned softmax scale gate that adaptively reweights the contributions of predefined contextual branches. The Edge-Aware Dynamic Gated FPN (EDG-FPN) decoder combines DySample-based feature alignment and dynamic gated fusion with a boundary-aware gate driven by an edge prediction branch, modulating high-level semantic propagation in boundary-sensitive regions without requiring additional edge annotations. On the Oil Spill Detection Dataset, SDE-Net achieves a 72.94% mIoU and 82.88% mDice, outperforming the UPerNet baseline equipped with the same ConvNeXtV2-Tiny backbone by 4.25 and 3.84 percentage points, respectively. The results demonstrate improved oil spill delineation and the preservation of sparse small-class structures under complex SAR sea surface conditions.