To facilitate responsive and cost-effective computing service delivery over edge networks, this paper investigates a novel two-stage double auction methodology via discovering an interesting idea of resource overbooking to overcome dynamic and uncertain nature of supply of edge servers (sellers) and demand generated from mobile devices (as buyers). The proposed auction integrates multiple essential goals such as maximizing social welfare as well as accelerating the decision-making process from both short-term and long-term perspectives (e.g., the time required to determine winning seller-buyer pairs), by introducing a stagewise strategy: an overbooking-driven pre-double auction (OPDAuction) for determining long-term cooperations between sellers and buyers before practical resource transactions as Stage I, and a real-time backup double auction (RBDAuction) for quickly coping with residual resource demands during actual transactions. In particular, by embedding a proper overbooking rate, OPDAuction helps with facilitating trading contracts between appropriate sellers and buyers as guidance for future transactions, by allowing the booked resources to exceed theoretical supply. Then, since pre-auctions may cause risks, our RBDAuction adjusts to real-time market changes, further enhancing the overall social welfare. More importantly, we offer an interesting view to show that our proposed two-stage auction can support significant design properties such as truthfulness, individual rationality, and budget balance. Extensive experiments demonstrate that our TwoSAuction achieves up to 76.8% reduction in decision-making time compared to conventional double auctions when considering 150 buyers and 25 sellers, while maintaining superior performance in social welfare and computational scalability over dynamic edge settings.