Vesicle gels have been investigated that are based on mixtures of classical nonionic surfactants with small amounts of ionic surfactants. Their rheological properties are largely controlled by the relative content of ionic surfactant in the mixture and the elastic properties go through a pronounced maximum for relatively low amounts of ionic surfactant content and depend in a systematic way on the total surfactant concentration. Depending on their composition their elastic moduli are typically in the range of 50-500 Pa and they have a yield stress of 1-20 Pa. The vesicle gels studied are able to solubilise large amounts of oils (up to more than 3 times the amount by mass of the surfactant) where the solubility depends to a large extent on the polarity of the oil and on the relative charge density of the surfactant mixture. We varied systematically the polarity of the solubilised oil and it is interesting to note that the maximum solubility occurs for the most hydrophobic oils while it is much less pronounced for more polar oils. The structural characterisation of these oil-swollen vesicle gels was done by means of static and dynamic light scattering, small-angle neutron scattering, electric conductivity, NMR self-diffusivity and electron microscopy. The vesicles bilayers are first swollen but for higher oil content the structure of individual vesicles is transformed into a bicontinuous structure. It is interesting to note that in that process no macroscopic phase separation takes place and also that the elastic properties are retained.