The Galactic object MWC 137 has been suggested to belong to the group of B[e] supergiants. However, with its large-scale optical bipolar ring nebula and high-velocity jet and knots, it is a rather atypical representative of this class. We performed multiwavelength observations spreading from the optical to the radio regimes. Based on optical imaging and long-slit spectroscopic data, we found that the northern parts of the large-scale nebula are predominantly blueshifted, while the southern regions appear mostly redshifted. We developed a geometrical model consisting of two double cones. Although various observational features can be approximated with such a scenario, the observed velocity pattern is more complex. Using near-infrared integral-field unit spectroscopy, we studied the hot molecular gas in the vicinity of the star. The emission from the hot CO gas arises in a small-scale disk revolving around the star on Keplerian orbits. Although the disk itself cannot be spatially resolved, its emission is reflected by the dust arranged in arc-like structures and the clumps surrounding MWC 137 on small scales. In the radio regime, we mapped the cold molecular gas in the outskirts of the optical nebula. We found that large amounts of cool molecular gas and warm dust embrace the optical nebula in the east, south, and west. No cold gas or dust was detected in the north and northwestern regions. Despite the new insights into the nebula kinematics gained from our studies, the real formation scenario of the large-scale nebula remains an open issue.