In this study, the rheological behavior and dynamic viscosity of 10W40 engine oil in the presence of ternary-hybrid nanomaterials of cerium oxide (CeO2), graphene oxide (GO), and silica aerogel (SA) were investigated experimentally. Nanofluid viscosity was measured over a volume fraction range of VF = 0.25–1.5%, a temperature range of T = 5–55 °C, and a shear rate range of SR = 40–1000 rpm. The preparation of ternary-hybrid nanofluids involved a two-step process, and the nanomaterials were dispersed in SAE 10W40 using a magnetic stirrer and ultrasonic device. In addition, CeO2, GO, and SA nanoadditives underwent X-ray diffraction-based structural analysis. The non-Newtonian (pseudoplastic) behavior of ternary-hybrid nanofluid at all temperatures and volume fractions is revealed by analyzing shear stress, dynamic viscosity, and power-law model coefficients. However, the nanofluids tend to Newtonian behavior at low temperatures. For instance, dynamic viscosity declines with increasing shear rate between 4.51% (at 5 °C) and 41.59% (at 55 °C) for the 1.5 vol% nanofluid. The experimental results demonstrated that the viscosity of ternary-hybrid nanofluid declines with increasing temperature and decreasing volume fraction. For instance, assuming a constant SR of 100 rpm and a temperature increase from 5 to 55 °C, the dynamic viscosity increases by at least 95.05% (base fluid) and no more than 95.82% (1.5 vol% nanofluid). Furthermore, by increasing the volume fraction from 0 to 1.5%, the dynamic viscosity increases by a minimum of 14.74% (at 5 °C) and a maximum of 35.94% (at 55 °C). Moreover, different methods (COMBI algorithm, GMDH-type ANN, and RSM) were used to develop models for the nanofluid's dynamic viscosity, and their accuracy and complexity were compared. The COMBI algorithm with R2 = 0.9995 had the highest accuracy among the developed models. Additionally, RSM and COMBI were able to generate predictive models with the least complexity.