This paper introduces SA-OOSC, a multimodal large language models (MLLM)-distilled semantic communication framework that achieves efficient semantic coding with scenario-aware importance allocations. This approach addresses a critical limitation of existing object-oriented semantic communication (OOSC) systems - assigning static importance values to specific classes of objects regardless of their contextual relevance. Our framework utilizes MLLMs to identify the scenario-augmented (SA) semantic importance for objects within the image. Through knowledge distillation with the MLLM-annotated data, our vectorization/de-vectorization networks and JSCC encoder/decoder learn to dynamically allocate coding resources based on contextual significance, i.e., distinguishing between high-importance objects and low-importance according to the SA scenario information of the task. The framework features three core innovations: a MLLM-guided knowledge distillation pipeline, an importance-weighted variable-length JSCC framework, and novel loss function designs that facilitate the knowledge distillation within the JSCC framework. Experimental validation demonstrates our framework's superior coding efficiency over conventional semantic communication systems, with open-sourced MLLM-annotated and human-verified datasets established as new benchmarks for future research in semantic communications.