In the paper, we study optimal transmission strategies in multi-channel opportunistic spectrum access (OSA) networks where one secondary user (SU) opportunistically accesses multiple orthogonal channels of primary users (PUs) under a continuous time Markov chain modeling of the channel occupancy by the PUs. Referred to as tunable threshold strategy, at a given time the SU chooses one channel of a given PU, decides if it should transmits or not and if so it protects the PU of this channel. To be operational, such a structure depends on the capability of the SU radio front-end to perform channel sensing. We consider one scenario where the SU node can simultaneously sense multiple channels and another scenario where the SU node can sense only one channel at a time. For each scenario, we develop the structure of the optimal transmission strategy and analyse the performance. We show that the optimal transmission strategy can be implemented using a simple tunable threshold algorithm.