Coherent Raman microscopy is the method of choice for label-free, real time characterization of the chemical composition in biomedical samples. The common implementation relies on scanning two tightly focused laser beams across the sample, which frequently leads to sample damage and proves slow over large fields of view. The few existing wide-field techniques for their part, feature a reduced lateral resolution and do not provide axial sectioning. To solve these practical limitations, we developed a robust wide-field nonlinear microscope that combines Random Illumination Microscopy (RIM) with coherent anti-Stokes Raman scattering (CARS) and sum frequency generation (SFG) contrasts. Based on a comprehensive theoretical study, CARS-RIMprovides super-resolved reconstructions and optical sectioning of the sample from the second-order statistics of multiple images obtained under different speckled illuminations. We experimentally show that multimodal CARS-RIM and SFG-RIM achieve wide-field nonlinear imaging with a 3 micron axial sectioning capability and a 300 nm transverse resolution, while effectively reducing the peak intensity at the sample compared to conventional point scanning CARS. We exemplify the label free, highly contrasted, chemical imaging potential of CARS-RIM and SFG-RIM wide-field microscopy in 2D, as well as 3D, for a variety of samples such as beads, unstained human breast tissue, and a mixture of chemical compounds.