We study nonreciprocity in a passive linear waveguide augmented with a local asymmetric, dissipative, and strongly nonlinear gate. Strong coupling between the constituent oscillators of the waveguide is assumed, resulting in broadband capacity for wave transmission. The local nonlinearity and asymmetry at the gate can yield strong global nonreciprocal acoustics, in the sense of drastically different acoustical responses depending on which side of the waveguide a harmonic excitation is applied. Two types of highly nonreciprocal responses are observed: (i) Monochromatic responses without frequency distortion compared to the applied harmonic excitation, and (ii) strongly modulated responses (SMRs) with strong frequency distortion. The complexification averaging (CX-A) method is applied to analytically predict the monochromatic solutions of this strongly nonlinear problem, and a stability analysis is performed to study the governing bifurcations. In addition, we build a machine learning framework where neural net (NN) simulators are trained to predict the performance measures of the gated waveguide in terms of certain transmissibility and nonreciprocity measures. The NN drastically reduces the required simulation time, enabling the determination of parameter ranges for desired performance in a high-dimensional parameter space. In the predicted desirable parameter space for nonreciprocity, the maximum transmissibility reaches 40%, and the transmitted energy varies by up to three orders of magnitude depending on the direction of wave transmission. The machine learning tools along with the analytical methods of this work can inform predictive designs of practical nonreciprocal waveguides and acoustic metamaterials that incorporate local nonlinear gates.