Understanding the chemistry of the interstellar medium (ISM) is fundamental for the comprehension of Galactic and stellar evolution. X-rays provide an excellent way to study the dust chemical composition and crystallinity along different sight lines in the Galaxy. In this work, we study the dust grain chemistry in the diffuse regions of the ISM in the soft X-ray band (<1 keV). We use newly calculated X-ray dust extinction cross sections obtained from laboratory data in order to investigate the oxygen K and iron L shell absorption. We explore the XMM-Newton and Chandra spectra of five low-mass X-ray binaries (LMXBs) located in the Galactic plane and model the gas and dust features of oxygen and iron simultaneously. The dust samples used for this study include silicates with different Mg:Fe ratios, sulfides, iron oxides, and metallic iron. Most dust samples are in both amorphous and crystalline lattice configuration. We computed the extinction cross sections using Mie scattering approximation and assuming a power-law dust size distribution. We find that the Mg-rich amorphous pyroxene (Mg_0.75Fe_0.25SiO₃) represents the largest fraction of dust towards most of the X-ray sources, namely about 70% on average. Additionally, we find that ~15% of the dust column density in our lines of sight is in metallic Fe. We do not find strong evidence for ferromagnetic compounds, such as Fe₃O₄ or iron sulfides (FeS, FeS₂). Our study confirms that iron is heavily depleted from the gas phase into solids; more than 90% of iron is in dust. The depletion of neutral oxygen is mild, namely of between 10% and 20% depending on the line of sight.