This paper analyzes and examines the ion sound and Langmuir waves (ISALWs) model with noise term utilizing the powerful extended tanh technique and the complete discrimination system for the polynomial method. Namely, we introduce some new stochastic solutions for the ISALWs model with multiplicative noise in the Itô sense. Ion sound waves and Langmuir waves are distinguished as fundamental plasma waves, characterized by varying frequencies, wavelengths, and modes of propagation. The combination of ion inertia and electron pressure results in the propagation of low-frequency electrostatic waves, referred to as ion sound waves, within a plasma. Langmuir waves refer to the high-frequency electrostatic oscillations of electrons within a plasma, while ions, due to their larger mass, are considered to be almost at rest. We also investigate how the noise term affects the structural characteristics of waves. These results have potential relevance to plasma physics applications, such as solar wind dynamics, Langmuir turbulence, and burst-like wave phenomena in cusp regions. Utilizing the capabilities of the MATLAB release, several profile pictures are created to demonstrate the behavior of the presented stochastic solutions. Ultimately, the suggested methodology has the potential to be adapted for various other models in the applied science.