We studied surface morphology and magnetic properties of Fe/MgO(001) films deposited at an angle varying between 0 degrees and 60 degrees with respect to the surface normal and with azimuth along the Fe or the Fe direction. Due to shadowing, elongated grains appear on the film surface for deposition at sufficiently large angle. X-ray reflectivity reveals that, depending on the azimuthal direction, films become either rougher or smoother for oblique deposition. For deposition along Fe the pronounced uniaxial magnetic anisotropy (UMA) results in the occurrence of "reversed" two-step and of three-step hysteresis loops. For deposition along Fe the growth-induced UMA is much weaker, causing a small rotation of the easy axes.