We present an atomistic study of the strain field, the one-particle electronic spectrum and the oscillator strength of the fundamental optical transition in chemically disordered InxGa1-xAs pyramidal quantum dots (QDs). Interdiffusion across the interfaces of an originally 'pure' InAs dot buried in a GaAs matrix is simulated through a simple model, leading to atomic configurations where the abrupt heterointerfaces are replaced by a spatially inhomogeneous composition profile x. Structural relaxation and the strain field calculations are performed through the Keating valence force field model, while the electronic and optical properties are determined within the empirical tight-binding approach. We analyze the relative impact of two different aspects of the chemical disorder, namely: (i) the effect of the strain relief inside the QD, and (ii) the purely chemical effect due to the group-III atomic species interdiffusion. We find that these effects may be quantitatively comparable, significantly affecting the electronic and optical properties of the dot. Our results are discussed in comparison with recent luminescence studies of intermixed QDs.