Microfluidic fabrication technologies are emerging as viable platforms for extracorporeal lung assist devices and oxygenators for cardiac surgical support and critical care medicine, based in part on their ability to more closely mimic the architecture of the human vasculature than existing technologies. In comparison with current hollow fiber oxygenator technologies, microfluidic systems have more physiologically-representative blood flow paths, smaller cross section blood conduits and thinner gas transfer membranes. These features can enable smaller device sizes and a reduced blood volume in the oxygenator, enhanced gas transfer efficiencies, and may also reduce the tendency for clotting in the system. Several critical issues need to be addressed in order to advance this technology from its current state and implement it in an organ-scale device for clinical use. Here we report on the design, fabrication and characterization of multilayer microfluidic oxygenators, investigating scaling effects associated with fluid mechanical resistance, oxygen transfer efficiencies, and other parameters in multilayer devices. Important parameters such as the fluidic resistance of interconnects are shown to become more predominant as devices are scaled towards many layers, while other effects such as membrane distensibility become less significant. The present study also probes the relationship between blood channel depth and membrane thickness on oxygen transfer, as well as the rate of oxygen transfer on the number of layers in the device. These results contribute to our understanding of the complexity involved in designing three-dimensional microfluidic oxygenators for clinical applications.