The results of gamma-ray observations of the binary system HESS J0632 + 057 collected during 450 hr over 15 yr, between 2004 and 2019, are presented. Data taken with the atmospheric Cherenkov telescopes H.E.S.S., MAGIC, and VERITAS at energies above 350 GeV were used together with observations at X-ray energies obtained with Swift-XRT, Chandra, XMM-Newton, NuSTAR, and Suzaku. Some of these observations were accompanied by measurements of the Hα emission line. A significant detection of the modulation of the very high-energy gamma-ray fluxes with a period of 316.7 ± 4.4 days is reported, consistent with the period of 317.3 ± 0.7 days obtained with a refined analysis of X-ray data. The analysis of data from four orbital cycles with dense observational coverage reveals short-timescale variability, with flux-decay timescales of less than 20 days at very high energies. Flux variations observed over a timescale of several years indicate orbit-to-orbit variability. The analysis confirms the previously reported correlation of X-ray and gamma-ray emission from the system at very high significance, but cannot find any correlation of optical Hα parameters with fluxes at X-ray or gamma-ray energies in simultaneous observations. The key finding is that the emission of HESS J0632 + 057 in the X-ray and gamma-ray energy bands is highly variable on different timescales. The ratio of gamma-ray to X-ray flux shows the equality or even dominance of the gamma-ray energy range. This wealth of new data is interpreted taking into account the insufficient knowledge of the ephemeris of the system, and discussed in the context of results reported on other gamma-ray binary systems.