Existing methods of non-intrusive load monitoring (NILM) in literatures generally suffer from high computational complexity and/or low accuracy in identifying working household appliances. This paper proposes an event-driven Factorial Hidden Markov model (eFHMM) for multiple appliances with multiple states in a household, aiming for low computational complexity and high load disaggregation accuracy. The proposed eFHMM decreases the computational complexity to be linear to the event number, which ensures online load disaggregation. Furthermore, the eFHMM is solved in two stages, where the first stage identifies state-changing appliance using transient signatures and the second stage confirms the inferred states using steady-state signatures. The combination of transient and steady-state signatures, which are extracted from transient and steady periods segmented by detected events, enhances the uniqueness of each state transition and associated appliances, which ensures accurate load disaggregation. The event-driven two-stage NILM solution, termed as eFHMM-TS, is naturally fit into an edge-cloud framework, which makes possible the real-world application of NILM. The proposed eFHMM-TS method is validated on the LIFTED and synD datasets. Results demonstrate that the eFHMM-TS method outperforms other methods and can be applied in practice.