Unveiling the physical nature of the oxygen-deficient conductive filaments (CFs) that are responsible for the resistive switching of the HfO2-based resistive random access memory (RRAM) devices represents a challenging task due to the oxygen vacancy related defect nature and nanometer size of the CFs. As a first important step to this goal, we demonstrate in this work direct visualization and a study of physico-chemical properties of oxygen-deficient amorphous HfO2-x by carrying out transmission electron microscopy electron holography as well as energy dispersive x-ray spectroscopy on HfO2/HfO2-x bilayer heterostructures, which are realized by reactive molecular beam epitaxy. Furthermore, compared to single layer devices, Pt/HfO2/HfO2-x /TiN bilayer devices show enhanced resistive switching characteristics with multilevel behavior, indicating their potential as electronic synapses in future neuromorphic computing applications.