The Galactic B[e] supergiant MWC137 is surrounded by a large-scale optical nebula. To shed light on the physical conditions and kinematics of the nebula, we analyze the optical forbidden emission lines [NII] {lambda}{lambda}6548,6583 and [SII] {lambda}{lambda}6716,6731 in long-slit spectra taken with ALFOSC at the Nordic Optical Telescope. The radial velocities display a complex behavior but, in general, the northern nebular features are predominantly approaching while the southern ones are mostly receding. The electron density shows strong variations across the nebula with values spreading from about zero to ~800cm^-3^. Higher densities are found closer to MWC137 and in regions of intense emission, whereas in regions with high radial velocities the density decreases significantly. We also observe the entire nebula in the two [SII] lines with the scanning Fabry-Perot interferometer attached to the 6m telescope of the Special Astrophysical Observatory. These data reveal a new bow-shaped feature at PA=225{deg}-245{deg} and a distance 80" from MWC137. A new H{alpha} image has been taken with the Danish 1.54m telescope on La Silla. No expansion or changes in the nebular morphology appear within 18.1yr. We derive a mass of 37_-5_^+9^M{sun} and an age of 4.7{+/-}0.8Myr for MWC137. Furthermore, we detect a period of 1.93d in the time series photometry collected with the TESS satellite, which could suggest stellar pulsations. Other, low-frequency variability is seen as well. Whether these signals are caused by internal gravity waves in the early-type star or by variability in the wind and circumstellar matter currently cannot be distinguished.