This paper reports on the demonstration of gate-tunable plasticity in artificial synaptic devices based on four-terminal planar memristors with amorphous gallium oxide as a memristive material. Reproducible resistance switching properties were obtained by applying voltages to the four terminals, indicating two-dimensional modulation of oxygen vacancy distribution. Based on the resistive switching properties, gate-tunable synaptic plasticity was successfully implemented by assigning read/write and gate roles to two pairs of diagonally arranged electrodes. Multilevel modulation of conductance change efficiency was demonstrated, mimicking neural functions of both excitatory principal neurons and inhibitory interneurons required for homeostatic plasticity in biological neural networks.