We investigate electronic and optoelectronic properties of few-layer palladium diselenide (PdSe2) phototransistors through spatially-resolved photocurrent measurements. A strong photocurrent resonance peak is observed at 1060 nm (1.17 eV), likely attributed to indirect optical transitions in few-layer PdSe2. More interestingly, when the thickness of PdSe2 flakes increases, more and more photocurrent resonance peaks appear in the near-infrared region, suggesting strong interlayer interactions in few-layer PdSe2 help open up more optical transitions between the conduction and valence bands of PdSe2. Moreover, gate-dependent measurements indicate that remarkable photocurrent responses at the junctions between PdSe2 and metal electrodes primarily result from the photovoltaic effect when a PdSe2 phototransistor is in the off-state and are partially attributed to the photothermoelectric effect when the device turns on. We also demonstrate PdSe2 devices with a Seebeck coefficient as high as 74 μV K-1 at room temperature, which is comparable with recent theoretical predications. Additionally, we find that the rise and decay time constants of PdSe2 phototransistors are ∼156 μs and ∼163 μs, respectively, which are more than three orders of magnitude faster than previous PdSe2 work and two orders of magnitude over other noble metal dichalcogenide phototransistors, offering new avenues for engineering future optoelectronics.