Memristors with programmable conductance are considered promising for energy-efficient analog memory and neuromorphic computing in edge AI systems. To improve memory density and computational efficiency, achieving multiple stable conductance states within a single device is particularly important. In this work, we demonstrate multilevel conductance tuning in few-layer tin hexathiophosphate (SnP2S6, SPS) memristors, achieving 325 stable states through a pulse-based programming scheme. By analyzing conductive filament evolution, we devised a voltage-pulse approach that effectively suppresses current noise, thereby maximizing the number of distinguishable states within the device ON/OFF ratio. Furthermore, we experimentally emulated synaptic plasticity behaviors including long-term potentiation and depression, and validated their performance through artificial neural network simulations on digit classification. These results highlight the potential of SPS memristors as high-resolution analog memory and as building blocks for neuromorphic computing, offering a pathway toward compact and efficient architectures for next-generation edge intelligence.