In order to fulfill the users' insatiable interests in accessing the Internet services and information wirelessly, one of key optimization techniques is caching frequently accessed the data items in a local cache. However, a strong consistency is implicitly assumed in most caching schemes but it may frequently occur a long query delay. In this paper, we propose a consistency-sensitive data access scheme to support applications' diverse consistency requirements, called ConSens, where a user can flexibly set its own consistency level. We also propose a lazy request and opportunistic data access techniques to effectively balance the data accessibility and query delay. Extensive performance studies indicate that the proposed techniques reduce the query delay and increase the number of opportunistic accesses significantly.