The response to strains is a crucial issue when applying two-dimensional (2D) materials in flexible electronic devices. Utilizing first-principles calculations based on density functional theory, we systematically studied the structural phase transition in niobium oxide diiodide $({\mathrm{NbOI}}_{2})$ monolayer and the consequent changes in electronic and magnetic properties. The calculated Young's modulus of the monolayer ${\mathrm{NbOI}}_{2}$ is approximately $80\phantom{\rule{0.16em}{0ex}}{\mathrm{Nm}}^{\text{\ensuremath{-}}1}$, and the in-plane Poisson's ratio is less than 0.1. Under uniaxial strain, dissociation of Nb atom dimers occurs, leading to a magnetic phase transition from nonmagnetic to antiferromagnetic states. Moreover, the coupling pattern of magnetic moments exhibits significant anisotropy along different directions with temperature variations. The exchange couplings in two orthogonal crystal directions were analyzed and the N\'eel temperature was predicted using Monte Carlo simulations. Additionally, the strain also modulates the ferroelectric polarization and switching barriers. A clear physical picture was provided to explain the magnetic and electronic mechanisms in the 2D ${\mathrm{NbOI}}_{2}$. This study shows the potential applications of such materials in future flexible microelectronic devices.