Complex electrical impedance and dielectric spectroscopy were applied to study the dielectric relaxations and their thermal behavior in ion-conducting composites/complexes from polymer poly(ethylene oxide) (PEO) and E8 nematic liquid crystals (LCs), at the compositional ratio PEO:E8 = 70:30 wt%. Flexible thin films of PEO/E8 with a thickness of 150 μm were inspected, as well as such films from Na+ ion-conducting electrolyte PEO/E8/NaIO4 with the same PEO:E8 compositional ratio, but additionally containing 10 wt.% from the salt sodium metaperiodate (NaIO4) as a dopant of Na+ ions. The molecular dynamics, namely the dielectric relaxation of PEO/E8 and PEO/E8/NaIO4, were characterized through analyses of complex impedance and dielectric spectra measured in the frequency range of 1 Hz–1 MHz, under variation of temperature from below to above the glass-transition temperature of these composites. The relaxation and polarization of dipole formations in PEO/E8 and PEO/E8/NaIO4 were evidenced and compared in terms of both electrical impedance and dielectric response depending on temperature. The results obtained for molecular organization, molecular relaxation dynamics, and electric polarization in the studied ion-conducting polymer/LC composites/complexes can be helpful in the optimization of their structure and performance, and are attractive for applications in flexible organic electronics, energy storage devices, and mechatronics.