High-moisture extrusion is a common process to impart an anisotropic, meat-like structure to plant proteins, such as wheat gluten. The addition of oil during the process promises to enhance the sensory properties of the meat analogs. In this study, the influence of oil on extrusion-relevant parameters as well as the structure-related characteristics of extruded wheat gluten was investigated. Oil was added directly to the extruder at different contents (0, 2, 4, 6%) and addition points (front/end of the extruder barrel). Process conditions, complex viscosity, Young’s modulus and oil phase morphology were determined as a function of oil content and oil addition point. With increasing oil content, material temperature, die pressure, and complex viscosity decreased. The addition of oil at the end of the extruder barrel reduced this effect compared to the addition of oil in the front part of the extruder. It was observed that the extrudate’s tensile strength is a function of material temperature, resulting in an increase in tensile strength with increasing material temperature. The oil was dispersed in the gluten matrix as small droplets with irregular shape. As the oil content increased, the size of the oil droplets increased, while the addition of oil at the end of the extruder resulted in a decrease in droplet size.