This work investigates the event-triggered control (ETC) problem for stochastic nonlinear systems with intermittent control (IC) and state quantization. ETC, state quantization, and aperiodically intermittent control (APIC) are incorporated into the control scheme to reduce the computational cost and communication load. Within the APIC framework, two control strategies are considered to examine their interactions: state quantization before event triggering (QbE) and state quantization after event triggering (QaE). Additionally, the Zeno phenomenon is avoided in the design of two static event-triggered mechanisms (ETMs). The known input-to-state stability (ISS) control law is supported by the system. Finite-time stability (FTS) and finite-time contraction stability (FTCS) are implemented. Each strategy guarantees the system's stability, and the appropriate scheme can be chosen by adjusting the length of the control interval. The effectiveness of the proposed ETC method is demonstrated through two numerical simulations.