Neuromorphic computing based on emerging devices could overcome the von Neumann bottleneck—the restriction created by having to transfer data between memory and processing units—and help deliver energy-efficient data processing. The van der Waals semiconductor α-phase indium selenide (α-In2Se3) offers ferroelectric, optoelectronic and semiconducting properties and is potentially an ideal substrate for information processing, but its physical properties are not well exploited. Here we report an optoelectronic synapse that is based on α-In2Se3 and has controllable temporal dynamics under electrical and optical stimuli. Tight coupling between ferroelectric and optoelectronic processes in the synapse can be used to realize heterosynaptic plasticity, with relaxation timescales that are tunable via light intensity or back-gate voltage. We use the synapses to create a multimode reservoir computing system with adjustable nonlinear transformation and multisensory fusion, which is demonstrated using a multimode handwritten digit-recognition task and a QR code recognition task. We also create a multiscale reservoir computing system via the tunable relaxation timescale of the α-In2Se3 synapse, which is tested using a temporal signal prediction task.