Auction is believed to be an effective way to solve or relieve the problem of radio spectrum shortage, by dynamically redistributing idle wireless channels of primary users to secondary users. However, to design a practical channel auction mechanism, we have to consider five challenges, including strategy-proofness, channel spatial reusability, channel heterogeneity, bid diversity, and social welfare maximization. Unfortunately, none of the existing works fully considered the five design challenges. In this paper, we present the first in-depth study on the problem of dynamic channel redistribution jointly considering the five design challenges, and present SMASHER, which is a family of Strategy-proof coMbinatorial Auction mechaniSms for HEterogeneous channel Redistribution. SMASHER contains two strategy-proof auction mechanisms, namely SMASHER-AP and SMASHER-GR. SMASHER-AP is a strategy-proof, approximately efficient combinatorial auction mechanism for indivisible channel redistribution. We further consider the case, in which channels can be shared by the users in a paradigm of time-division multiplexing and propose SMASHER-GR, which is a strategy-proof channel allocation and scheduling mechanism. We have extensively evaluated our designs. The evaluation results show that our designs achieve much better performance than existing works.