Strong physical gels derived from thermoplastic elastomeric ABA triblock copolymers solvated with a midblock-selective oil continue to find use in increasingly diverse applications requiring highly elastic and mechanically robust soft materials with tunable properties. In this study, we first investigate the morphological characteristics of thermoplastic elastomer gels (TPEGs) derived from a homologous series of linear A(BA)(n) multiblock copolymers composed of styrene and hydrogenated isoprene repeat units and possessing comparable molecular weight but varying in the number of B-blocks: 1 (triblock), 2 (pentablock), and 3 (heptablock). Small-angle X-ray scattering performed at ambient temperature confirms that (i) increasing hydrogenation reduces the microdomain periodicity of the neat copolymers and (ii) increasing the oil concentration of the TPEGs tends to swell the nanostructure (increasing the periodicity), but concurrently decreases the size of the styrenic micelles, to different extents depending on the molecular architecture. Complementary dissipative particle dynamics simulations reveal the level to which midblock bridging, which is primarily responsible for the elasticity in this class of materials, is influenced by both oil concentration and molecular architecture. Since constrained topological complexity increases with increasing block number, we introduce a midblock conformation index that facilitates systematic classification of the different topologies involved in nearest-micelle bridge formation. Those possessing at least one bridged and one looped midblock with no dangling ends are found to be the most predominant topologies in the pentablock and heptablock networks.