An interferometric displacement sensor with useful properties has been built based on a laser with optical feedback from light that is backscattered by a moving object. Information about the object's motion is encoded in the phase of the backscattered light, which in turn influences the phase and the amplitude of the laser via injection-locking physics. We derive the properties of the amplitude and phase modulation of the laser from standard injection-locking relations augmented by a self-consistency condition. These predictions are then confirmed by experimental results. An off-the-shelf two-mode frequency-stabilized laser is used in two different interferometric configurations. First, the amplitude modulation of the laser is utilized for displacement measurements in a homodyne setup. Second, the phase modulation of the laser is used in a pseudoheterodyne interferometer. In both cases, the backscattered light from the object can be injected into the laser cavity without the help of any focusing optics. Thus the injection-locked sensor combines the advantages of readily available equipment and a straightforward optical setup without need for intricate alignment, and thereby meets two important conditions for industrial applications.