Here we present first-principles calculations to investigate systematically the electronic behavior and the electron energy low-loss spectra (EELS) of monolayer, bilayer, four-layer, and bulk configurations of periodic GaX (X = S, Se), as well as the effect of mechanical strain on the electronic properties of the GaX monolayer. We predicate that the GaX monolayer is a semiconductor with an indirect band gap, however, the difference between the direct and indirect gaps is so small that electrons can transfer easily between this minimum with a small amount of thermal energy. Owning to strong surface effects, the electronic and dielectric properties of GaX vary drastically with number of layers in a sheet. In detail, the band gap increases from multilayer-to-single layer and EELS shifts towards larger wavelengths with a decrease in the layer thickness. Moreover, we demonstrate that the band gaps of GaX monolayers can be widely tuned by mechanical deformation, making them potential candidates for tunable nanodevices. The present study provides theoretical insight leading to a better understanding of these novel 2D structures.