We report on a systematic study of the composition and structure of GaAs/InAs/GaAs quantum wells using Auger Electron Spectroscopy (AES), Extended Energy Loss Fine Structure (EELFS), and Reflection High Energy Electron Diffraction (RHEED) techniques. Double heterostructures with InAs thickness ranging from 2 to 10 monolayers, capped by 2 to 10 monolayers of GaAs, were grown by MBE using a variety of techniques, including those employing sequential, interrupted, and delayed shutter timing sequences. AES peak ratios are compared with model calculations to monitor compositional development of the multilayers. The AES results are correlated with RHEED measurements to determine MBE growth parameters for optimal control of the stoichiometry and surface morphology. EELFS was used to monitor strain in the buried InAs layers. The AES results show departure from smooth laminar growth of layers of stoichiometric InAs on GaAs at temperatures below 420 C and above 470 C. AES results on the quantum well structures suggest floating InAs layers on top of the GaAs and/or facet formation in the GaAs layers. The EELFS results, when compared to bulk InAs, indicate the presence of strain in the buried InAs quantum well.