Epitaxial FeGa/IrMn bilayers with exchange biases along the FeGa[100] and [110] directions are prepared on MgO(001) single crystal substrates by magnetron sputtering through controlling the orientation of the external field in situapplied during growth. The effect of the exchange bias orientation on the magnetic switching process and the magnetic switching field are studied. The X-ray φ-scan indicates that the FeGa layer is epitaxially grown with a 45° in-plane rotation on the MgO(001) substrate along the FeGa(001)[110] direction and the MgO(001)[100] direction. The measurements of the angular dependence of the ferromagnetic resonance field and the corresponding fitting to the Kittel equation show that the samples have a superposition of fourfold symmetric magnetocrystalline anisotropy $ {K}_{1} $ , unidirectional magnetic exchange bias anisotropy $ {K}_{\mathrm{e}\mathrm{b}} $ , and uniaxial magnetic anisotropy $ {K}_{\mathrm{u}} $ with configuration of $ {K}_{\mathrm{e}\mathrm{b}}//\left[100\right] $ or $ {K}_{\mathrm{e}\mathrm{b}}//\left[110\right] $ . The combined longitudinal and transverse magneto-optical Kerr effect measurements show that sample with $ {K}_{\mathrm{e}\mathrm{b}}//\left[100\right] $ exhibits square loops, asymmetrically shaped loops, and one-sided two-step loops in different external magnetic field directions. In contrast, the sample with $ {K}_{\mathrm{e}\mathrm{b}}//\left[110\right] $ exhibits one-sided two-step and two-sided two-step loops as the magnetic field orientation changes. Because the $ {K}_{1} $ is superimposed by $ {K}_{\mathrm{u}} $ and $ {K}_{\mathrm{e}\mathrm{b}} $ , the in-plane fourfold symmetry of the magnetic anisotropy energy is broken. The local minima are no longer strictly along the in-plane $ \left\langle{100}\right\rangle $ directions, but make a deviation angle which depends on the relative orientation and strength of magnetic anisotropy. A model based on the domain wall nucleation and propagation is proposed with considering the different orientations of $ {K}_{\mathrm{e}\mathrm{b}} $ , which can nicely explain the change of the magnetic switching route with the magnetic field orientation and fit the angular dependence of the magnetic switching fields, indicating a significant change of domain wall nucleation energy as the orientation of $ {K}_{\mathrm{e}\mathrm{b}} $ changes.