Aims. We study the EUV/soft X-ray emission generated by charge transfer between solar wind heavy ions and interstellar neutral atoms and variations of the X-ray intensities and spectra with the line of sight direction, the observer location, the solar cycle phase and the solar wind anisotropies, and a temporary enhancement of the solar wind similar to the event observed by Snowden et al. (2004) during the XMM-Hubble Deep Field North exposure. Methods. Using recent observations of the neutral atoms combined with updated cross-sections and cascading photon spectra we have computed self-consistent distributions of interstellar hydrogen, helium and highly charged solar wind ions for a stationary solar wind and we have constructed monochromatic emission maps and spectra. We have evaluated separately the contribution of the heliosheath and heliotail, and included X-ray emission of the excited solar wind ions produced in sequential collisions to the signal. Results. In most practicable observations, the low and medium latitude X-ray emission is significantly higher at minimum activity than at maximum, especially around December. This occurs due to a strong depletion of neutrals during the high activity phase, which is not compensated by an increase of the solar wind flux. For high latitudes the emission depends on the ion species in a complex way. Intensity maps are in general significantly different for observations separated by six-month intervals. Secondary ions are found to make a negligible contribution to the X-ray line of sight intensities, because their density becomes significant only at large distances. The contribution of the heliosheath-heliotail is always smaller than 5%. We can reproduce both the intensity range and the temporal variation of the XMM-HDFN emission lines in the 0.52-0.75 keV interval, using a simple enhanced solar wind spiral stream. This suggests a dominant heliospheric origin for these lines, before, during and also after the event.