The goal of this work is to study the evolution of thermoelectric transport across the members of the Ruddlesden-Popper series iridates [Formula: see text], where a metal-insulator transition driven by bandwidth change occurs, from the strongly insulating Sr2IrO4 to the metallic non Fermi liquid behavior of SrIrO3. Sr2IrO4 ([Formula: see text]), Sr3Ir2O7 ([Formula: see text]) and SrIrO3 ([Formula: see text]) polycrystals are synthesized at high pressure and characterized by structural, magnetic, electric and thermoelectric transport analyses. We find a complex thermoelectric phenomenology in the three compounds. Thermal diffusion of charge carriers accounts for the Seebeck behavior of Sr2IrO4, whereas additional drag mechanisms come into play in determining the Seebeck temperature dependence of Sr3Ir2O7 and SrIrO3. These findings reveal a close relationship between magnetic, electronic and thermoelectric properties, strong coupling of charge carriers with phonons and spin fluctuations as well as the relevance of multiband description in these compounds.