Wireless sensor networks are widely used to perform measurement and monitoring tasks in large sensing fields. Several applications require every point in the monitored area to be covered by at least \emph{k} sensors (\emph{k-coverage} problem) for measurement accuracy or robustness. In heterogeneous multi-functional sensor networks \emph{p} parallel observation tasks are performed with \emph{p} types of sensors, each task having its own $k_i ( i=1, 2, ... p)$ coverage requirement, assuming that multi-functional sensors are used which may have multiple measurement capabilities (\emph{multi-$k$-coverage} problem). In order to prolong the lifetime of the network, active and sleeping states of sensors can be altered while maintaining the required coverage for all sensing tasks. In this paper an efficient distributed sensor state scheduling algorithm for multi-functional WSNs is proposed to solve the multi-$k$-coverage problem. The proposed multi-functional Controlled Greedy Sleep (mCGS) algorithm is the generalization of a recently proposed quasi-optimal scheduling algorithm. It is easy to implement and solves the common scheduling problem of heterogeneous multi-functional sensor networks. It has low local communication overhead and can adapt to dynamic changes in the network, while the required network-wide coverage for all sensing tasks is guaranteed as long as it is physically possible. The performance and the fault tolerance of the algorithm is illustrated by simulation examples.