Magnetically ordered insulators are of key interest for spintronics applications, but most of them have not yet been explored in depth regarding their magnetic properties, in particular with respect to their dynamic response. We study the static and dynamic magnetic properties of epitaxially strained γ-Fe2O3 (maghemite) thin films grown via pulsed-laser deposition on MgO substrates by SQUID magnetometry and cryogenic broadband ferromagnetic resonance experiments. SQUID magnetometry measurements reveal hysteretic magnetization curves for magnetic fields applied both in- and out of the sample plane. From the magnetization dynamics of our thin films, we find a small negative effective magnetization in agreement with a strain induced perpendicular magnetic anisotropy. Moreover, we observe a non-linear evolution of the ferromagnetic resonance-linewidth as a function of the microwave frequency and explain this finding with the so-called slow relaxor model. We investigate the magnetization dynamics and non-linear damping mechanisms present in our samples as a function of frequency and temperature and in particular, observe a sign change in the effective magnetization from the transition of the magnetic anisotropy from a perpendicular easy axis to an easy in-plane anisotropy for reduced temperatures. Its nonlinear damping properties and strain-induced perpendicular anisotropy render γ-Fe2O3 an interesting material platform for spintronics devices.