We study the 0.57 keV (O VII triplet) and 0.65 keV (O VIII) diffuse emission generated by charge transfer collisions between solar wind (SW) oxygen ions and interstellar H and He neutral atoms in the inner Heliosphere. These lines which dominate the 0.3-1.0 keV energy interval are also produced by hot gas in the galactic halo (GH) and possibly the Local Interstellar Bubble (LB). We developed a time-dependent model of the SW Charge-Exchange (SWCX) X-ray emission, based on the localization of the SW Parker spiral at each instant. We include input SW conditions affecting three selected fields, as well as shadowing targets observed with XMM-Newton, Chandra and Suzaku and calculate X-ray emission fot O VII and O VIII lines. We determine SWCX contamination and residual emission to attribute to the galactic soft X-ray background. We obtain ground level intensities and/or simulated lightcurves for each target and compare to X-ray data. The local 3/4 keV emission (O VII and O VIII) detected in front of shadowing clouds is found to be entirely explained by the CX heliospheric emission. No emission from the LB is needed at these energies. Using the model predictions we subtract the heliospheric contribution to the measured emission and derive the halo contribution. We also correct for an error in the preliminary analysis of the Hubble Deep Field North (HDFN).