We report the tunable conducting behavior of a series of ${(\mathrm{S}{\mathrm{r}}_{2}\mathrm{Ir}{\mathrm{O}}_{4})}_{4}/{(\mathrm{S}{\mathrm{r}}_{3}\mathrm{R}{\mathrm{u}}_{2}{\mathrm{O}}_{7})}_{N}$ ($N$ = 1, 2, and 4) atomic layer superlattices, in which phases of itinerant electrons, itinerant holes, localized electrons, and an anomalous charge region can be varied dependent on the period and the temperature. Specifically, for the $N$ = 4 superlattice, the electron-to-hole transition occurs at a temperature of 35 K, at which the sample behaves as an intrinsic insulator without either electrons or holes. Upon further reducing the temperature to below 16 K, the superlattice enters an anomalous phase region in which an abrupt zero-to-negative magnetoresistance transition and a Hall resistivity kink are observed at 1.3 and 2.1 T, respectively. Above these fields, polarized neutron reflectivity measurements revealed ferromagnetism confined in the $\mathrm{S}{\mathrm{r}}_{3}\mathrm{R}{\mathrm{u}}_{2}{\mathrm{O}}_{7}$ layers. Moreover, the $N$ = 2 superlattice exhibits a bump feature in the anomalous Hall resistivity near 1.3 T, which is similar to the previously reported topological Hall phenomenon in ultrathin $\mathrm{SrRu}{\mathrm{O}}_{3}$ heterostructures. We demonstrate that the layered $4d/5d$ oxide superlattice is a powerful platform in engineering exotic types of phases which have not been explored in their thin-film or bulk samples.