Double auctions play a pivotal role in stimulating active participation of a large number of users comprising both task requesters and workers in mobile crowdsourcing. However, most existing studies have concentrated on designing offline two-sided auction mechanisms and supporting single-type tasks and fixed auction service models. Such works ignore the need of dynamic services and are unsuitable for large-scale crowdsourcing markets with extremely diverse demands (i.e., types and urgency degrees of tasks required by different requesters) and supplies (i.e., task skills and online durations of different workers). In this paper, we consider a practical crowdsourcing application with an on-demand service strategy. Especially, we innovatively design three online service models, namely online single-bid single-task (OSS), online single-bid multiple-task (OSM) and online multiple-bid multiple-task (OMM) models to accommodate diversified tasks and bidding demands for different users. Furthermore, to effectively allocate tasks and facilitate bidding, we propose a truthful online double auction mechanism for each service model based on the McAfee double auction. By doing so, each user can flexibly select auction service models and corresponding auction mechanisms according to their current interested tasks and online duration. To illustrate this, we present a three-demand example to explain the effectiveness of our on-demand service strategy in realistic crowdsourcing applications. Moreover, we theoretically prove that our mechanisms satisfy truthfulness, individual rationality, budget balance and consumer sovereignty. Through extensive simulations, we show that our mechanisms can accommodate the various demands of different users and improve social utility including platform utility and average user utility. IEEE