A study of the absorption spectra of excitons in ZnSe-ZnS strained layer superlattices (SLS) with well widths ranging from 0.6 to 7.6 nm is reported. The n=1 heavy hole (hh) and light hole (1h) exciton absorptions are clearly resolved for all samples even near room temperature. A theoretical estimation of the n=1 hh exciton peak energy, which takes account of strain, quantum confinement of free carriers, and exciton binding energy enhancement by reduced dimensionality, is in excellent agreement with the experimental results. The variations in absorption linewidth and energy shift between absorption and emission band peaks, as a function of quantum well width, have also been measured: the experimental results provide evidence that the origin of the so-called ``Stokes' shift'' lies in Anderson localization due to monolayer fluctuations in the well width. The temperature dependence of the exciton peak energy and its linewidth are interpreted in terms of electron-phonon and exciton-phonon interactions.