The intermetallic quasi-one-dimensional binary superconductor V₂Ga₅ was recently found to exhibit a topologically nontrivial normal state, making it a natural candidate for a topological superconductor. By combining dc-magnetization, nuclear magnetic resonance, and muon-spin rotation (µSR) measurements on high-quality V₂Ga₅ single crystals, we investigate the electronic properties of its normal- and superconducting ground states. NMR measurements in the normal state indicate a strong anisotropy in both the line shifts and the relaxation rates. Such anisotropy persists also in the superconducting state, as shown by the magnetization and µSR-spectroscopy results. In the latter case, data collected at different temperatures, pressures, and directions of the magnetic field (with respect to the crystalline axes) evidence a fully-gapped, strongly anisotropic superconductivity. At the same time, hydrostatic pressure is shown to only lower the Tc value, but not to change the superfluid density nor its temperature dependence. Lastly, we discuss the search for topological signatures in the normal state of V₂Ga₅, as well as a peak splitting in the FFT of the µSR spectrum, possibly related to an unconventional vortex lattice. Our results suggest that V₂Ga₅ is a novel system, whose anisotropy plays a key role in determining its unusual electronic properties.