In this article, we propose a novel stochastic event-driven near-optimal sliding-mode controller design for addressing the consensus of a multiagent system in a network. The system is prone to external disturbances and network uncertainties, such as losses and delays of data packets. The randomness of network uncertainties introduces stochasticity in the system. The design starts with the formulation of control-affine dynamics based on a single integrator robot model, formation error, and sliding surface dynamics. An event-triggering condition is then derived for an update of control input for each agent. These input updates guarantee desired consensus in finite time with reaching time of each agent's sliding surface having an upper bound. The admissibility of event-driven near-optimal control updates is also ensured for each agent. The near-optimal control design for each agent has achieved through neural-network-based actor-critic architecture. The implementation of Pioneer P3-DX mobile robots illustrates threefold efficacy of the proposed design: 1) advantages of event-driven approach and higher order sliding mode controller; 2) robustness to network uncertainties; and 3) near-optimality in system performance.