Received signal strength (RSS) based source localization method is popular due to its simplicity and low cost. However, this method is highly dependent on the propagation model which is not easy to be captured in practice. Moreover, most existing works only consider the single source and the identical measurement noise scenario, while in practice multiple co-channel sources may transmit simultaneously, and the measurement noise tends to be nonuniform. In this paper, we study the multiple co-channel sources localization (MSL) problem under unknown nonuniform noise, while jointly estimating the parametric propagation model. Specifically, we model the MSL problem as being parameterized by the unknown source locations and propagation parameters, and then reformulate it as a joint parametric sparsifying dictionary learning (PSDL) and sparse signal recovery (SSR) problem which is solved under the framework of sparse Bayesian learning with iterative parametric dictionary approximation. Furthermore, multiple snapshot measurements are utilized to improve the localization accuracy, and the Cramer-Rao lower bound (CRLB) is derived to analyze the theoretical estimation error bound. Comparing with the state-of-the-art sparsity-based MSL algorithms as well as CRLB, extensive simulations show the importance of jointly inferring the propagation parameters,and highlight the effectiveness and superiority of the proposed method.