Silicon photonic integrated devices used for nonlinear optical signal processing play a key role in ultrafast switching, computing, and modern optical communications. However, current devices suffer from limited operation speeds and low conversion efficiencies due to the intrinsically low nonlinear index of silicon. In this paper, we experimentally demonstrate enhanced optical nonlinearity in a silicon–organic hybrid slot waveguide consisting of an ultranarrow slot waveguide coated with a highly nonlinear organic material. The fabricated slot area is as narrow as 45 nm, which is, to the best of our knowledge, the narrowest slot width that has been experimentally reported in silicon slot waveguides. The nonlinear coefficient of the proposed device with a length of 3 mm is measured to be up to 1.43×106W-1km-1. Based on the nanostructure design, the conversion efficiencies of degenerate four-wave mixing showed enhancements of more than 12 dB and 5 dB compared to those measured for an identical device without the organic material and a silicon strip waveguide, respectively. As a proof of concept, all-optical canonical logic units based on the prepared device with two inputs at 40 Gb/s are analyzed. The obtained logic results showed clear temporal waveforms and wide-open eye diagrams with error-free performance, illustrating that our device has great potential for use in high-speed all-optical signal processing and high-performance computing in the nodes and terminals of optical networks.