We present new intermediate-band Strömgren photometry based on more than 300 u, v, b, y images of the Galactic globular cluster ω Cen. Optical data were supplemented with new multiband near-infrared (NIR) photometry (350 J, H, Ks images). The final optical-NIR catalog covers a region of more than 20 × 20 arcmin squared across the cluster center. We use different optical-NIR color-color planes together with proper-motion data available in the literature to identify candidate cluster red-giant (RG) stars. By adopting different Strömgren metallicity indices, we estimate the photometric metallicity for ≈4000 RGs, the largest sample ever collected. The metallicity distributions show multiple peaks ([Fe/H]phot = -1.73 ± 0.08, -1.29 ± 0.03, -1.05 ± 0.02, -0.80 ± 0.04, -0.42 ± 0.12, and -0.07 ± 0.08 dex) and a sharp cutoff in the metal-poor (MP) tail ([Fe/H]phot lsim -2 dex) that agree quite well with spectroscopic measurements. We identify four distinct subpopulations, namely, MP ([Fe/H] <= -1.49), metal-intermediate (MI; -1.49 < [Fe/H] <= -0.93), metal-rich (MR; -0.95 < [Fe/H] <= -0.15), and solar metallicity ([Fe/H] ≈ 0). The last group includes only a small fraction of stars (~8% ± 5%) and should be confirmed spectroscopically. Moreover, using the difference in metallicity based on different photometric indices, we find that the 19% ± 1% of RGs are candidate CN-strong stars. This fraction agrees quite well with recent spectroscopic estimates and could imply a large fraction of binary stars. The Strömgren metallicity indices display a robust correlation with α-elements ([Ca+Si/H]) when moving from the MI to the MR regime ([Fe/H] gsim -1.7 dex). Based on observations collected in part with the 1.54 m Danish Telescope and with the NTT@ESO Telescope operated in La Silla, and in part with the VLT@ESO Telescope operated in Paranal. The Strömgren data were collected with DFOSC2@Danish (proprietary data), while the NIR data were collected with SOFI@NTT, proposals: 66.D-0557 and 68D-0545 (proprietary data), 073.D-0313 and 59.A-9004 (ESO Science archive) and with ISAAC@VLT, proposal 075.D-0824 (proprietary data).