Theoretical calculations with real-space pseudopotentials constructed within density-functional theory are employed to calculate mechanical and electronic properties for [100], [110], and [111] germanium nanowires up to 2.7 nm in diameter. Uniaxial strain is applied to wires within the range of to 5. The strain energy is used to calculate the Young's modulus for each wire, whose values are found to increase with diameter up to approximately the theoretical bulk values. Electronic band structures are calculated for each wire with respect to strain, and from these structures band gaps are obtained. The size and the nature (direct or indirect) of the band gaps are found to be influenced by the growth direction, wire size, and strain amount. Carrier effective masses are calculated from the band structures and may be discontinuous under certain amounts of strain owing to band crossing, which can correspond to sudden drops in carrier mobilities.