The equation of state, dynamical properties, and molecular-scale structure of squalane and mixtures of poly-α-olefins at room temperature are studied with a combination of state-of-the-art, high-pressure experiments and molecular-dynamics simulations. Diamond-anvil cell experiments indicate that both materials are non-hydrostatic media at pressures above ∼1 GPa. The equation of state does not exhibit any sign of a first-order phase transition. High-pressure x-ray diffraction experiments on squalane show that there are no Bragg peaks, and hence, the apparent solidification occurs without crystallization. These observations are complemented by a survey of the equation of state and dynamical properties using simulations. The results show that molecular diffusion is essentially arrested above about 1 GPa, which supports the hypothesis that the samples are kinetically trapped in metastable amorphous-solid states. The shear viscosity becomes extremely large at very high pressures, and the coefficient governing its increase from ambient pressure is in good agreement with the available literature data. Finally, simulated radial distribution functions are used to explore the evolution of the molecular-scale structure with increasing pressure. Subtle changes in the short-range real-space correlations are related to a collapse of the molecular conformations with increasing pressure, while the evolution of the static structure factor shows excellent correlation with the available x-ray diffraction data. These results are of indirect relevance to oil-based lubricants, as the pressures involved are comparable to those found in engines, and hence, the ability of lubricating thin films to act as load-bearing media can be linked to the solidification phenomena studied in this work.