We present a nonlinear rheological investigation of model rod-like particles at the air/water interface in dilatation and shear. Cellulose nanocrystals were modified to vary their surface hydrophobicity, creating a range of surface-active particles with varying contact angle. The interfacial rheological properties were studied using a series of frequency sweeps in small amplitude oscillatory shear as well as strain sweeps under large amplitude oscillatory shear (LAOS) and large amplitude oscillatory dilatation (LAOD) to include the nonlinear behavior. A multi-mode Maxwell model was used to fit the frequency sweeps that were obtained during formation of the interfacial layer. A shift toward longer relaxation times was found, more pronounced for particles with higher hydrophobicity. Lissajous plots in LAOS revealed strain stiffening, yielding, and unconstrained flow of the interfacial layers. Lissajous plots in LAOD revealed strain hardening in compression and strain softening in expansion, increasing with surface pressure and with particle hydrophobicity. While interfacial layers commonly show gel or solid-like behavior, our findings imply a weakly aggregated system. The rheological behavior indicates the formation of larger clusters for particles with high hydrophobicity compared to smaller clusters for particles with low hydrophobicity. The particle-particle interactions therefore vary with hydrophobicity, suggesting that capillary interactions are important for the formation of these microstructures.