Ram-pressure stripping of the spiral galaxy ESO 137−001 within the highly dynamical intracluster medium (ICM) of the Norma cluster lead to spectacular extraplanar CO, optical, Hα, UV, and X-ray emission. The Hα and X-ray tails extend up to 80 kpc from the galactic disk. We present dynamical simulations of the ram-pressure stripping event, and investigate the physics of the stripped gas and its ability to form stars. We also use these simulations to predict H I maps and to constrain the orbit of ESO 137−001 within the Norma cluster. Special care was taken for the stripping of the diffuse gas. In a new approach, we analytically estimate the mixing between the intracluster and interstellar media. Different temporal ram-pressure profiles and the ICM-ISM mixing rate were tested. Three preferred models show most of the observed multiwavelength characteristics of ESO 137−001. Our highest-ranked model best reproduces the CO emission distribution, velocity for distances of ≲20 kpc from the galactic disk, and the available near-ultraviolet (NUV) observations. The second and third preferred models best reproduce the available X-ray and Hα observations of the gas tail, including the Hα velocity field. The angle between the direction of the galaxy’s motion and the plane of the galactic disk is between 60° and 75°. Ram-pressure stripping thus occurs more face-on. The existence of a two-tailed structure is a common feature in our models, and is due to the combined action of ram pressure and rotation together with the projection of the galaxy on the sky. Our modeling of the Hα emission caused by ionization through thermal conduction is consistent with observations. We predict the H I emission distributions for the different models. Based on the 3D velocity vector derived from our dynamical model, we derive a galaxy orbit, which is close to unbound. We argue that ram pressure is enhanced by a factor of ∼2.5 compared to that expected for an orbit in an unperturbed spherical ICM. This increase can be obtained in two ways: an increase in the ICM density or a moving ICM opposite to the motion of the galaxy within the cluster. In a strongly perturbed galaxy cluster, such as the Norma cluster, with an off-center ICM distribution, the two possibilities are probable and plausible.