We report ultra-high-resolution observations (R approximate to 9 x 10(5)) of Na I, Ca II, K I, CH and CH+ for interstellar sightlines towards 12 bright stars in Orion. These data enable the detection of many more absorption components than previously recognized, providing a more accurate perspective on the absorbing medium. This is especially so for the line of sight to the Orion nebula, a region not previously studied at very high resolution. Model fits have been constructed for the absorption-line profiles, providing estimates for the column density, velocity dispersion and central velocity for each constituent velocity component. A comparison between the absorption occurring in sightlines with small angular separations has been used, along with comparisons with other studies, to estimate the line-of-sight velocity structures. Comparisons with earlier studies have also revealed temporal variability in the absorption-line profile of zeta Ori, highlighting the presence of small-scale spatial structure in the interstellar medium on scales of approximate to 10 au. where absorption from both Na-0 and K-0 is observed for a particular cloud, a comparison of the velocity dispersions measured for each of these species provides rigorous limits on both the kinetic temperature and turbulent velocity prevailing in each cloud. Our results indicate the turbulent motions to be subsonic in each case. Na-0/Ca+ abundance ratios are derived for individual clouds, providing an indication of their physical state.