In this study, shear thickening fluid (STF) samples with different mass fractions were prepared by uniformly dispersing high-purity spherical silica powder in the polyethylene glycol (PEG) medium using the ball milling process. The influence of nano-particles on the shear and compression thickening effects of the STF dispersion system was investigated through the addition of fumed silica. Furthermore, the ball milled carbonyl iron powders (CIPs) with different particle sizes were dispersed uniformly in the STFs to prepare magnetorheological-STF (MR-STF) samples. The rheological properties of the developed STF and MR-STF samples were studied experimentally through a rheometer, and the results show that a lower temperature leads to a more obvious shear thickening effect of the STFs and that a smaller critical shear rate value promotes this effect. A higher content of silica powder also causes a more significant shear thickening effect of the STFs. Moreover, the addition of nano-fumed silica can significantly enhance the shear thickening effect, and the transition from continuous to discontinuous STFs can be realized by increasing the fumed silica mass fraction. Similarly, higher contents of silica powder and nano-fumed silica in the compression mode result in a more obvious thickening effect. In addition, the size of the CIP particles and the magnetic field strength directly affect the shear thickening effect of the MR-STFs. Specifically, under the same ferromagnetic particle mass fraction, the larger the CIP particles, the higher the applied magnetic induction intensity. Although a significant MR effect can be obtained, a certain inhibitory weakening effect is produced for the shear thickening behavior of the MR-STFs. Finally, considering the results in combination with the hydro-clustering and jamming theories, a mechanism was established to reveal the influence of different silica powder contents and nano-fumed silica fillings on the shear and compression thickening effects of STFs. Besides, a mechanism was proposed for the inhibition of the shear thickening effect of the MR-STFs by the ordered structures formed by CIP particles of different sizes in a magnetic field.