We present a space-angle dual multiplexing holographic recording system for realizing single-exposure multi-wavelength optical diffraction tomographic (ODT) imaging. This system is achieved by combining the principle of single-exposure multi-wavelength holographic imaging technique based on angle-division multiplexing with the principle of single-exposure ODT imaging technique based on microlens array multi-angle illuminations and space-division multiplexing. Compared with the existing multi-wavelength ODT imaging methods, it enables the holographic recording of all the diffraction tomography information of a measured specimen at multiple illumination wavelengths in a single camera exposure without any scan mechanism. Using our proposed data processing method, the multi-wavelength three-dimensional (3D) refractive index tomograms of a specimen can be eventually reconstructed from single recorded multiplexing hologram. Experimental results of a static polystyrene bead and a living C. elegans worm demonstrate the feasibility of this system.