Delay-tolerant Wi-Fi offloading is known to improve overall mobile network bandwidth at low delay and low cost. Yet, in reality, we rarely find mobile apps that fully support opportunistic Wi-Fi access. This is mainly because it is still challenging to develop delay-tolerant mobile apps due to the complexity of handling network disruptions and delays. In this paper, we present Cedos, a practical delay-tolerant mobile network access architecture in which one can easily build a mobile app. Cedos consists of three components. First, it provides a familiar socket API whose semantics conforms to TCP, while the underlying protocol, (DTP)-T-2, transparently handles network disruptions and delays in mobility. Second, Cedos allows the developers to explicitly exploit delays in mobile apps. App developers can express maximum user-specified delays in content download or use the API for real-time buffer management at opportunistic Wi-Fi usage. Third, for backward compatibility to existing TCP-based servers, Cedos provides D(2)Prox, a protocol-translation Web proxy. D2Prox allows intermittent connections on the mobile device side, but correctly translates Web transactions with traditional TCP servers. We demonstrate the practicality of Cedos by porting mobile Firefox and VLC video streaming client to using the API. We also implement delay/disruption-tolerant podcast client and run a field study with 50 people for eight weeks. We find that up to 92.4% of the podcast traffic is offloaded to Wi-Fi, and one can watch a streaming video in a moving train while offloading 48% of the content to Wi-Fi without a single pause.