During the last years there is a growing interest in the use of nonsquare quantum wells (QW) with nonlinear graded bandgap profiles. In this paper, the influence of interdiffusion and strain on the optical absorption characteristic in InxGa1-xAs/GaAs quantum wells is investigated by an exciton Green's function method. Our model takes into account both the continuum and bound states due to the Coulomb interaction between electrons and holes in the excitonic absorption spectrum. The interdiffusion process modifies the As-grown square quantum well into an error-function compositional profile, and it leads to important changes in the energy bandgap and the heavy hole (HH)-light hole (LH) energy splitting caused by the strain effects. These changes in the optical properties of interdiffused QW's produce an overall blue shift of the optical absorption edge that provides a wavelength tuning range useful for optoelectronic applications. For most of the different material parameters involved in the analysis we use expressions and data from the literature, and include others, such as the excitonic linewidth, that are estimated by us. With this model we can show the influence of the diffusion length and the As-grown Indium mole fraction and well width on the absorption characteristics of these structures. This can help us in tailoring the absorption edge of disordered structures to desired wavelengths.