We combine F115W and F277W images collected with the Near Infrared Camera of the James Webb Space Telescope with multiband, multi-epoch Hubble Space Telescope observations of omega Centauri to investigate its multiple stellar populations and internal kinematics. Our study focuses on a region spanning about 0.9 to 2.3 half-light radii from the cluster center, which is largely unexplored by these telescopes. Using chromosome maps, we identified the principal populations along the upper main sequence and among M dwarfs, distinguishing lower-stream stars chemically akin to first-generation globular cluster stars with similar metallicities from upper-stream stars enriched in helium and nitrogen but oxygen poor. Both streams also host subpopulations with varying metallicities. We found radially anisotropic motions, with upper-stream stars exhibiting significantly stronger anisotropy than lower-stream stars. Subdividing the upper stream into extreme and intermediate light-element populations revealed a gradient in anisotropy, with intermediate stars lying between the lower-stream stars and extreme upper-stream populations. However, metal-rich and metal-poor stars within each stream show moderate kinematic differences. The lower-stream stars show a higher angular momentum dispersion compared to upper-stream stars, and they also exhibit stronger systemic rotation and proper motion skewness, further highlighting their kinematic divergence. Finally, leveraging a mass range of about 0.15 to 0.7 solar masses, we detected a low degree of energy equipartition for all cluster stars, which decreases with radial distance from the cluster center.