In this article, we establish several infinite families of Ramanujan-type congruences modulo 16, 32 and 64 for $\overline{p}_o(n)$, the number of overpartitions of $n$ in which only odd parts are used. In this paper, we prove a coupled fixed point theorem, using the concept of simulation function, which generalizes the works of Bhaskar et al., Sintunavarat et al. and Zlatanov. The validity of main results is verified through interesting examples. As sequel we also prove that the theorem has a vital application in solving a system of nonlinear impulsive fractional stochastic differential equations.