With the increasing adoption of AI applications such as large language models and computer vision AI, the computational demands on AI inference systems are continuously rising, making the enhancement of task processing capacity using existing hardware a primary objective in edge clouds. We propose EPARA, an end-to-end AI parallel inference framework in edge, aimed at enhancing the edge AI serving capability. Our key idea is to categorize tasks based on their sensitivity to latency/frequency and requirement for GPU resources, thereby achieving both request-level and service-level task-resource allocation. EPARA consists of three core components: 1) a task-categorized parallelism allocator that decides the parallel mode of each task, 2) a distributed request handler that performs the calculation for the specific request, and 3) a state-aware scheduler that periodically updates service placement in edge clouds. We implement a EPARA prototype and conduct a case study on the EPARA operation for LLMs and segmentation tasks. Evaluation through testbed experiments involving edge servers, embedded devices, and microcomputers shows that EPARA achieves up to 2.1$\times$ higher goodput in production workloads compared to prior frameworks, while adapting to various edge AI inference tasks.