The signals generated by various third-order nonlinear spectroscopies (transient absorption, transient grating, and three-pulse photon echo peak shift) on energy transfer systems are investigated by carrying out model calculations. Focusing on the understanding of basic features, we employ a simple model system consisting of pairs of energy donors and acceptors. We assume that energy transfer occurs via the Forster mechanism (weak electronic coupling). Static disorder in the transition energies of the chromophores induces inhomogeneities in the rate of energy transfer and in the optical response. The interplay between these two processes is discussed. We show that the peak shift experiment has advantages over the other types of experiment in clarifying the nature of disorder which affects the mechanism and time scale of energy transfer. For example, the peak shift technique can reveal the extent to which disorder is correlated in individual chromophore assemblies, and the extent to which energy transfer can correlate the energies of donors and acceptors. Finally the ability of the peak shift method to distinguish and quantify diagonal and off-diagonal disorder in energy transfer systems is discussed.