We use ideal fluid energy conditions to constrain the free parameter of the degree of nonconservation ζ of the energy-momentum tensor in Rastall gravity theory. We study the mass-radius relation of strange stars and the corresponding stability using the obtained range of ζ constrained by energy conditions. In our calculations, we use the MIT bag model with a color-flavor-locked state to describe strange quark matter. We obtain a finite, narrow range of 0≤ζ≤0.5. In addition to ζ, the corresponding nonconservation of the energy-momentum tensor depends on the gradient of the energy-momentum scalar. The behavior of matter in the MIT bag model is one example in which the energy-momentum tensor is conserved through the zero value on the gradient of the energy-momentum scalar. We also find that the corresponding mass-radius relation of strange stars depends on the interplay of matter parameters, such as ms, B, Δ, and the Rastall parameter ζ. In addition, we find that as ζ increases, the maximum strange star mass decreases. Furthermore, the stability of strange stars with regard to radial oscillations in Rastall gravity theory is rather different from that in general relativity because of the impact of the nonconservation of the energy-momentum tensor. The stability boundary mass and radius determined from the zero modes of radial perturbation oscillations are not the same as the maximum mass and corresponding radius. This is because the Rastall nonconservation term increases the matter pressure to support the strange star against collapse, especially when vs2>1/3. The reverse applies when vs2<1/3.