We consider transmission of correlated sources over multiuser channels where the receiver(s) have access to correlated side information. Our goal is to characterize necessary and sufficient conditions for lossless transmission and uncover scenarios where separation of source and channel coding, either in the traditional 'informational' sense (where both source and channel encoders and decoders are designed independently) or in the 'operational' sense (where the encoders are independent, but the source and channel decoding is done jointly), is optimal. We first study a multiple access channel where the source signals are independent given the receiver side information. We prove an informational source channel separation theorem for this communication system. We next investigate source and channel coding for the compound multiple access and interference channels. We give general sufficient conditions for lossless transmission of each source for both channels, and then provide necessary conditions that hold under certain assumptions on the nature of the source and the receiver side information. For the interference channel, the necessary conditions hinge on a strong source-channel interference condition which depends not only on the channel but on the source and side information correlations as well. Our results suggest the optimality of informational or operational separation depending on the correlation structure of the side information and the amount of interference.