We present a study of the large-scale spatial distribution of 6482 RASS X-ray sources in approximately 5000 deg^2 in the direction of Orion. We examine the astrophysical properties of a sub-sample of ~100 optical counterparts, using optical spectroscopy. This sub-sample is used to investigate the space density of the RASS young star candidates by comparing X-ray number counts with Galactic model predictions. We characterize the observed sub-sample in terms of spectral type, lithium content, radial and rotational velocities, as well as iron abundance. A population synthesis model is then applied to analyze the stellar content of the RASS in the studied area. We find that stars associated with the Orion star-forming region do show a high lithium content. A population of late-type stars with lithium equivalent widths larger than Pleiades stars of the same spectral type (hence younger than ~70-100 Myr) is found widely spread over the studied area. Two new young stellar aggregates, namely "X-ray Clump 0534+22" (age~2-10 Myr) and "X-ray Clump 0430-08" (age~2-20 Myr), are also identified. The spectroscopic follow-up and comparison with Galactic model predictions reveal that the X-ray selected stellar population in the direction of Orion is characterized by three distinct components, namely the clustered, the young dispersed, and the widespread field populations. The clustered population is mainly associated with regions of recent or ongoing star formation and correlates spatially with molecular clouds. The dispersed young population follows a broad lane apparently coinciding spatially with the Gould Belt, while the widespread population consists primarily of active field stars older than 100 Myr. We expect the "bi-dimensional" picture emerging from this study to grow in depth as soon as the distance and the kinematics of the studied sources will become available from the future Gaia mission. ; Comment: 17 pages, 13 figures, 4 tables. Accepted for publication in Astronomy and Astrophysics. Abstract shortened