Ram pressure stripping (RPS) is an important mechanism for galaxy evolution. In this work, we present results from HST and APEX observations of one RPS galaxy, ESO 137-002 in the closest rich cluster Abell 3627. The galaxy is known to host prominent X-ray and H α tails. The HST data reveal significant features indicative of RPS in the galaxy, including asymmetric distribution of dust in the galaxy, dust filaments, and dust clouds in ablation generally aligned with the direction of ram pressure, and young star clusters immediately upstream of the residual dust clouds that suggest star formation (SF) triggered by RPS. The distribution of the molecular gas is asymmetric in the galaxy, with no CO upstream and abundant CO downstream and in the inner tail region. A total amount of ∼5.5 × 109 M⊙ of molecular gas is detected in the galaxy and its tail. On the other hand, we do not detect any active SF in the X-ray and H α tails of ESO 137-002 with the HST data and place a limit on the SF efficiency in the tail. Hence, if selected by SF behind the galaxy in the optical or UV (e.g. surveys like GASP or using the Galex data), ESO 137-002 will not be considered a 'jellyfish' galaxy. Thus, galaxies like ESO 137-002 are important for our comprehensive understanding of RPS galaxies and the evolution of the stripped material. ESO 137-002 also presents a great example of an edge-on galaxy experiencing a nearly edge-on RPS wind. © 2021 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society.