The vectorial four-wave mixing response of an individual strongly confined exciton-biexciton system with fine-structure splitting in a GaAs/AlGaAs quantum dot is measured by dual-polarization heterodyne spectral interferometry. The results are compared with theoretical predictions based on the optical Bloch equations. The system is described by a fourlevel scheme, which is a model system of the nonlinear excitonic response in low-dimensional semiconductors. We measure its coherence properties and determine the underlying dephasing mechanisms. An impact of the inhomogeneous broadening by spectral wandering on the coherent response is investigated. We further discuss the different four-wave mixing pathways, polarization selection rules, the time-resolved polarization state, the vectorial response in two-dimensional four-wave mixing and ensemble properties.