We have investigated superlattices consisting of up to 30 epitaxial nanomultilayers (3-7 nm thick) of ferromagnetic La2/3Ca 1/3MnO3 (LCMO) and insulating SrTiO3 (STO) hybrids. The superlattices demonstrate dramatic shifts of Curie temperature, indicating the possibility of its tunability. The metal-insulator transition (MIT) has been observed around 140 K. Below the MIT temperature, the superlattices have shown sharp drops of resistivity, facilitating the largest and sharpest magnetoresistance peaks (>2000%) ever observed in LCMO films and superlattices at low temperatures. The observed experimental results can be explained in the frame of the phase separation model in manganites with well-organized structures. The results of magnetic and transport measurements of such hybrid structures are discussed, indicating a magnetodielectric effect in STO interlayers. The magnetic and transport properties of the superlattices are shown to be technology-dependent, experiencing dimensional transitions, which enables the creation of structures with prescribed magnetoresistance characteristics for a broad range of applications.