The Kitaev material α-RuCl3 is among the most prominent candidates to host a quantum spin-liquid state endowed with fractionalized excitations. Recent experimental and theoretical investigations have separately revealed the importance of both the magnetoelastic coupling and the magnetic anisotropy in dependence of the applied magnetic-field direction. In this combined theoretical and experimental research, we investigate the anisotropic magnetic and magnetoelastic properties for magnetic fields applied along the main crystallographic axes as well as for fields canted out of the honeycomb plane. We found that the magnetostriction anisotropy is unusually large compared to the anisotropy of the magnetization, which is related to the strong magnetoelastic Γ′-type coupling in our ab-initio derived model. We observed large, nonsymmetric magnetic anisotropy for magnetic fields canted out of the honeycomb ab plane in opposite directions, namely, toward the +c∗ or -c∗ axes, respectively. The observed directional anisotropy is explained by considering the relative orientation of the magnetic field with respect to the coaligned RuCl6 octahedra. Magnetostriction measurements in canted fields support this nonsymmetric magnetic anisotropy; however, these experiments are affected by magnetic torque effects. Comparison of theoretical predictions with experimental findings allow us to recognize the significant contribution of torque effects in experimental setups where α-RuCl3 is placed in canted magnetic fields.