This paper aims to seek the performative stable solution and the optimal solution of the distributed stochastic optimization problem with decision-dependent distributions, which is a finite-sum stochastic optimization problem over a network and the distribution depends on the decision variables. For the performative stable solution, we provide an algorithm, DSGTD-GD, which combines the distributed stochastic gradient tracking descent method with the greedy deployment scheme. Under the constant step size policy, we show that the iterates generated by DSGTD-GD converge linearly, in expectation, to a neighborhood of the performative stable solution. Under the diminishing step size policy, we show that the iterates generated by DSGTD-GD converge to the performative stable solution with rate $\mathcal{O}\left(\frac{1}{k}\right)$. Moreover, we establish that the deviation between the averaged iterates of DSGTD-GD and the performative stable solution converges in distribution to a normal random vector. For the optimal solution, we provide an algorithm, DSGTD-AG, which combines the distributed stochastic gradient tracking descent method with the adaptive gradient scheme. Under the constant step size policy, we show that the iterates generated by DSGTD-AG converge to a stationary solution with rate of $\mathcal{O}(\frac{\ln K}{\sqrt{K}})$, where $K$ is the number of iterations. The effectiveness of DSGTD-GD and DSGTD-AG is further demonstrated numerically with synthetic and real-world data.