This paper proposes an information filtering-based distributed fusion for nonlinear uncertain systems with multiplicative random parameters and randomly delayed measurements in sensor networks. This is a typical nonlinear and non-Gaussian stochastic system with multiple uncertainties including nonlinearity, multiplicative random parameters and random delay, along with additive noises. In the criterion of minimizing the mean square error of state estimate, the centralized information-type filter via Gaussian mixture realization is put forward, by applying statistical linear regression to nonlinear measurement models to reconstruct a new and equivalent one with the linear form. Then, the distributed implementation is designed via average consensus with the corresponding weight of each component being updated distributively, in order to ensure that the Gaussian mixture distribution of the posterior probability density in each processing unit asymptotically approximates the corresponding one in the centralized fusion as closely as possible. Meanwhile, the d-step lag state smoothing is obtained to further improve the estimation precision, in terms of the proposed filtering method. An example with multiplicative random parameters and one-step/two-step random delay in the distributed processing network is simulated to validate the proposed method.