The size, shape and strain dependences of the electronic properties of germanium nanowires (GeNWs) along the <112> direction are investigated using first-principles calculations based on density functional theory. The structures of relatively stable <112> GeNWs of different sizes have been revealed. The <112> GeNWs exhibit direct band gaps when the cross-sectional aspect ratio of the (111) to the (110) facet is larger than 1. For a relatively high stability of the <112> GeNWs, the compressive strain tends to widen the band gap, whereas tensile strain tends to narrow it. The variation in band gaps originates from the different responses of valence and conduction bands to externally applied strain. Our results demonstrate that size, shape and strain can be used in unison to effectively tune the band structures of GeNWs, providing useful guidance for designing future nanoelectronic devices.