Radiation source (RS) localization is crucial in electromagnetic environmental monitoring. Existing methods require prior knowledge of the environment and have overlooked the impact of multipath effects. Their positioning accuracy is penalized in practical applications. This paper presents an environment cognition-based variational Bayesian positioning method, which can achieve precise multi-source localization in uncooperative multipath environments using only the measurements of received signal strength (RSS). We begin by leveraging the signal propagation properties to design a model-data integrated unsupervised learning network, which partitions the positioning area according to the transmission states of different multipath signals. To estimate the number of RSs and mitigate the multipath effect, we identify the data samples of multipath RSS and divide them into groups, each corresponding to an RS. Then, a new variational Bayesian positioning algorithm is developed to operate without prior channel information and locate multiple RSs accurately across varying signal propagation models. Simulations show that our positioning method can effectively improve the accuracy of multi-RS localization by 10% in uncooperative multipath environments, compared to the state-of-the-art RSS-based localization techniques.