This article investigates the qualitative analysis and traveling wave solutions of the stochastic nonlinear Kodama equation within the Stratonovich framework. By applying a random traveling wave transformation, the equation is first converted into an ordinary differential equation. The qualitative behavior of the corresponding two-dimensional dynamical system and its perturbation is then examined using planar dynamical system analysis. Subsequently, the complete discriminant system method is employed to derive four distinct types of optical solutions. Three-dimensional plots illustrating these solutions under different parameters are also presented.