Amphiphilic block copolymers can self-assemble in the presence of selective solvents ("water" and "oil") into a variety of different microstructures. The role that "oil" plays in the phase behavior and structure of copolymer-oil-water systems is the focus of the present investigation. We examined a poloxamer-type poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer (Pluronic F127 : E100P70E100) in ternary isothermal systems with water and each of three "oils" (of varying polarity), p-xylene, n-butyl acetate and butan-1-ol. A total of six phases with different microstructures have been identified in the ternary systems studied here : normal (oil-in-water) micellar cubic (I-1), normal hexagonal (H-1), lamellar (L-alpha), and reverse (water-in-oil) hexagonal(H-2) lyotropic liquid crystals, and normal micellar (L-1) and reverse micellar (L-2) solutions. The number and types of phases, as well as the composition range of their stability, are different for each ternary system, reflecting the effects of oil. Systematic small-angle X-ray scattering (SAXS) measurements have been performed in order to establish the structure of the phases and determine their characteristic length-scales. The location of the "oils" in the different self-assembled microstructures has been deduced from the structural dimensions obtained from SAXS and the constraints imposed by the copolymer total volume fraction and interfacial area : all xylene is present in the interior (apolar core) of the oil-in-water microdomains and butanol is located at the interfacial region between poly(propylene oxide) and poly(ethylene oxide), while butyl acetate contributes to both the core and the interfacial domains.