We employ first principles methods based on density functional theory and beyond to study CdSexTe1-x alloys in the zincblende and wurtzite structures. From the cluster expansion formalism, we provide a detailed phase diagram showing a consolute temperature of 325 K, above which miscibility may be achieved. In the random solid solution, a zincblende-to-wurtzite phase boundary is found to range from Se concentrations of x = 0.5-0.6, in agreement with experiment, owing to increasing ionic character of the Cd-anion bonds. Disordered CdSexTe1-x configurations are modeled using special quasirandom structures, for which optoelectronic properties are computed with the hybrid HSE06 functional. Alloying is shown to cause strong bowing effects in the band gap and effective electron/hole masses, which we attribute to local structural distortions as illustrated by analysis of bond length distributions. Downward bowing in the band gap and effective hole mass of the zincblende structure is highlighted for its potential benefits in photovoltaics through increased net photocurrent. Absorption coefficients and reflectivity are also reported, showing promising results in zincblende CdSexTe1-x as indicated by substantial optical absorption throughout all Se concentrations. Lastly, we identify the presence of short-range order in CdSexTe1-x characterized by clustering among like atoms in order to minimize strain. The degree of clustering, which may be tuned by temperature, also controls the magnitude of the band gap. Therefore, we propose both composition and short-range order as effective tools to be utilized in the design and synthesis of improved solar cell absorber layer materials.