In all van der Waals layered antiferromagnetic semiconductors investigated so far, a negative magnetoresistance has been observed in vertical transport measurements, with characteristic trends that do not depend on applied bias. Here, we report vertical transport measurements on a layered antiferromagnetic semiconductor CrPS 4 that exhibit a drastically different behavior, namely, a strongly bias-dependent, positive magnetoresistance that is accompanied by pronounced oscillations for devices whose thickness is smaller than 10 nm. We establish that this unexpected behavior originates from transport being space-charge limited and not injection limited as for the layered antiferromagnetic semiconductors studied earlier. Our analysis indicates that the positive magnetoresistance and the oscillations only occur when electrons are injected into in-gap defect states, whereas when electrons are injected into the conduction band, the magnetoresistance vanishes. We propose a microscopic explanation for the observed phenomena that combines concepts typical of transport through disordered semiconductors with known properties of the CrPS 4 magnetic state, thus capturing all basic experimental observations. Our results illustrate the need to understand, in detail, the nature of transport through vdW magnets in order to extract information about the nature of the order magnetic states and its microscopic properties.