Organic matter is responsible for the generation of hydrocarbons during the thermal maturation of source rock formation. This geochemical process engenders a network of organic hosted pores that governs the flow of hydrocarbons from the organic matter to fractures created during the stimulation of production wells. Therefore, it can be reasonably assumed that predictions of potentially recoverable confined hydrocarbons depend on the geometry of this pore network. Here, we analyze mesoscale structures of three organic porous networks at different thermal maturities. We use electron tomography with subnanometric resolution to characterize their morphology and topology. Our 3D reconstructions confirm the formation of nanopores and reveal increasingly tortuous and connected pore networks in the process of thermal maturation. We then turn the binarized reconstructions into lattice models including information from atomistic simulations to derive mechanical and confined fluid transport properties. Specifically, we highlight the influence of adsorbed fluids on the elastic response. The resulting elastic energy concentrations are localized at the vicinity of macropores at low maturity whereas these concentrations present more homogeneous distributions at higher thermal maturities, due to pores' topology. The lattice models finally allow us to capture the effect of sorption on diffusion mechanisms with a sole input of network geometry. Eventually, we corroborate the dominant impact of diffusion occurring within the connected nanopores, which constitute the limiting factor of confined hydrocarbon transport in source rocks.