Localization is a vital service in underwater acoustic sensor networks (UASNs). Autonomous underwater vehicles (AUVs), with their mobility and collaborations can provide accurate, extensive, and efficient localization service for large-scale UASNs. During localization, AUVs travel along the predefined paths and broadcast reference messages to aid sensor nodes in estimating locations. However, AUVs-aided localization faces the following two challenges: 1) complex localization path planning for multiple AUVs, which requires consideration of localization accuracy and optimization of travel path simultaneously and 2) harsh underwater localization conditions, such as unsynchronized clocks and stratification effects seriously affect the localization accuracy. To this end, an efficient AUVs-aided localization scheme (EAL) is proposed for large-scale UASNs, which jointly addresses the path planning and localization in an unified framework. Specifically, we propose a graph-based localization path planning mechanism, which considers the impact of path on localization and determines effective travel paths for AUVs. Furthermore, we design an iteration-based asynchronous localization mechanism, which could compensate the stratification effect and achieve accurate localization for the sensor nodes. Extensive simulation results show that the EAL can achieve efficient and high accuracy localization for the sensor nodes with the aid of multiple AUVs.