Nonlinear partial differential equations serve as key components for the mathematical representation of engineering phenomena across several domains within the known universe. In the field of engineering difficulties, the most significant considerations are invariably systems composition and physics of components. In this regard, the impact of noise emerges as a crucial aspect. Building on this foundational understanding, this study aims to present a novel version of the stochastic Lakshmanan–Porsezian–Daniel equation with higher order dispersion in fiber Bragg gratings. The equation incorporates multiplicative white noise in the Itô sense. To investigate this new model, we employ a couple of integration techniques which are the enhanced Kudryashov method and the generalized sine–Gordon equation method. Bright and singular solitons are achieved through the enhanced Kudryashov method, while straddled bright–dark solitons and straddled singular–singular solitons are obtained using the generalized sine–Gordon equation method. Solutions in the context of Jacobi’s elliptic functions are also considered. The emergence of all possible solutions using the proposed techniques has been noticed, each accompanied by specific constraints that guarantee their existence. Moreover, the effect of noise intensity on soliton dynamics is investigated and interpreted by simulating the graphical representations.