In this paper, aiming at securing range query, top-k query, and skyline query in tiered sensor networks, we propose the Secure Range Query (SRQ), Secure Top-$k$ Query (STQ), and Secure Skyline Query (SSQ) schemes, respectively. In particular, SRQ, by using our proposed \emph{prime aggregation} technique, has the lowest communication overhead among prior works, while STQ and SSQ, to our knowledge, are the first proposals in tiered sensor networks for securing top-$k$ and skyline queries, respectively. Moreover, the relatively unexplored issue of the security impact of sensor node compromises on multidimensional queries is studied; two attacks incurred from the sensor node compromises, \emph{collusion attack} and \emph{false-incrimination attack}, are investigated in this paper. After developing a novel technique called \emph{subtree sampling}, we also explore methods of efficiently mitigating the threat of sensor node compromises. Performance analyses regarding the probability for detecting incomplete query-results and communication cost of the proposed schemes are also studied.