Single crystals as well as polycrystalline samples of GaNbO4, Ga(Ta,Nb)O-4, and GaTaO4 were grown from the melt and by solid-state reactions, respectively, at various temperatures between 1698 and 1983 K. The chemical composition of the crystals was confirmed by wavelength dispersive electron microprobe analysis, and the crystal structures were determined by single-crystal X-ray diffraction. In addition, a high-P-T synthesis of GaNbO4 was performed at a pressure of 2 GPa and a temperature of 1273 K. Raman spectroscopy of all compounds as well as Rietveld refinement analysis of the powder X-ray diffraction pattern of GaNbO4 were carried out to complement the structural investigations. Density functional theory (DFT) calculations enabled the assignment of the Raman bands to specific vibrational modes within the structure of GaNbO4. To determine the hardness (H) and elastic moduli (E) of the compounds, nanoindentation experiments have been performed with a Berkovich diamond indenter tip. Analyses of the load-displacement curves resulted in a high hardness of H = 11.9 +/- 0.6 GPa and a reduced elastic modulus of E-r = 202 +/- 9 GPa for GaTaO4. GaNbO4 showed a lower hardness of H = 9.6 +/- 0.5 GPa and a reduced elastic modulus of E-r = 168 +/- 5 GPa. Spectroscopic ellipsometry of the polished GaTa0.5Nb0.5O4 ceramic sample was employed for the determination of the optical constants n and k. GaTa0.5Nb0.5O4 exhibits a high average refractive index of n(D) = 2.20, at lambda = 589 nm. Furthermore, in situ high-temperature powder X-ray diffraction experiments enabled the study of the thermal expansion tensors of GaTaO4 and GaNbO4, as well as the ability to relate them with structural features.