Emerging applications, such as robot-assisted eldercare and object recognition, generally employ deep learning neural networks (DNNs) models and naturally require: i) handling streaming-in inference requests and ii) adapting to possible deployment scenario changes. Online model fine-tuning is widely adopted to satisfy these needs. However, fine-tuning involves significant energy consumption, making it challenging to deploy on edge devices. In this paper, we propose EdgeOL, an edge online learning framework that optimizes inference accuracy, fine-tuning execution time, and energy efficiency through both inter-tuning and intra-tuning optimizations. Experimental results show that, on average, EdgeOL reduces overall fine-tuning execution time by 82%, energy consumption by 74%, and improves average inference accuracy by 1.70% over the immediate online learning strategy.