Federated learning (FL) is a machine learning paradigm where a shared central model is learned across distributed edge devices while the training data remains on these devices. Federated Averaging (FedAvg) is the leading optimization method for training non-convex models in this setting with a synchronized protocol. However, the assumptions made by FedAvg are not realistic given the heterogeneity of devices. In particular, the volume and distribution of collected data vary in the training process due to different sampling rates of edge devices. The edge devices themselves also vary in their available communication bandwidth and system configurations, such as memory, processor speed, and power requirements. This leads to vastly different training times as well as model/data transfer times. Furthermore, availability issues at edge devices can lead to a lack of contribution from specific edge devices to the federated model. In this paper, we present an Asynchronous Online Federated Learning (ASO-Fed) framework, where the edge devices perform online learning with continuous streaming local data and a central server aggregates model parameters from clients. Our framework updates the central model in an asynchronous manner to tackle the challenges associated with both varying computational loads at heterogeneous edge devices and edge devices that lag behind or dropout. We perform extensive experiments on a simulated benchmark image dataset and three real-world non-IID streaming datasets. The results demonstrate the effectiveness of \model~on converging fast and maintaining good prediction performance.