We have identified a class of two-dimensional ferroelastic monolayers, denoted as InXY (where X = S, Se; Y = Cl, Br, I), through first-principles calculations. The dynamic, thermal, and mechanical stabilities of these InXY monolayers are validated by phonon dispersion spectra, AIMD calculations, and elastic constants, respectively. These monolayers exhibit semiconducting behavior with bandgaps ranging from 1.94 to 2.85 eV and possess excellent ferroelasticity with strong ferroelastic signals and moderate ferroelastic switching barriers. Notably, the band edge positions of InSBr and InSI monolayers are observed to stride the water redox potentials at pH = 0, indicating their potential as photocatalysts for water splitting in acidic environments. We also explored the effects of biaxial strain on the band edge alignments and photocatalytic performance of these monolayers. Moreover, the InXY monolayers exhibit excellent anisotropic optical absorption across the visible to ultraviolet regions, along with high anisotropic carrier transport. The coupling of ferroelastic and anisotropic properties in these monolayers offers promising opportunities for designing controllable electronic devices, thereby expanding their potential applications in multifunctional materials. Our findings reveal that the InXY monolayers are promising candidates for efficient photocatalytic water splitting and controllable optoelectronic applications.