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Long-context large language models (LLMs) enable applications that reason over hundreds of thousands to millions of tokens, but serving these workloads efficiently is challenging. Modern systems cache key-value (KV) states and rely on hierarchical context caching across GPU HBM, CPU memory, and SSDs. We show that naïve designs often become I/O-bound: fragmented KV layouts lead to small transfers that underutilize bandwidth, cache loading stalls prefill, and schedulers that ignore cache-loading latency and delay hits (concurrent requests for the same context during a cache miss) suffer severe throughput degradation. We present Strata, a hierarchical context caching framework for long-context LLM serving. Strata introduces a GPU-assisted I/O mechanism that decouples GPU and host layouts to enable efficient large transfers, and a cache-aware scheduler that mitigates delay hits, balances batches to hide cache-loading latency, and opportunistically overlaps complementary work. Implemented as part of SGLang and deployed in production, Strata improves throughput by up to 5× over vLLM-LMCache and 3.75× over NVIDIA TensorRT-LLM, without hurting short-context performance.