We present the Hubble imaging Probe of Extreme Environments and Clusters (HiPEEC) survey. We fit HST NUV to NIR broad-band and H alpha fluxes to derive star cluster ages, masses, and extinctions and determine the star formation rate (SFR) of six merging galaxies. These systems arc excellent laboratories to trace cluster formation under extreme gas physical conditions, rare in the local Universe, but typical for star-forming galaxies at cosmic noon. We detect clusters with ages of 1-500 Myr and masses that exceed 10(7) M-circle dot. The recent cluster formation history and their distribution within the host galaxies suggest that systems such as NGC 34, NGC 1614, and NGC 4194 are close to their final coalescing phase, while NGC 3256, NGC 3690, and NGC 6052 are at an earlier/intermediate stage. A Bayesian analysis of the cluster mass function in the age interval 1-100 Myr provides strong evidence in four of the six galaxies that an exponentially truncated power law better describes the observed mass distributions. For two galaxies, the fits arc inconclusive due to low number statistics. We determine power-law slopes beta similar to -1.5 to -2.0 and truncation masses, M-c, between 10(6) and a few times 10(7) M-circle dot, among the highest values reported in the literature. Advanced mergers have higher M-c than early/intermediate merger stage galaxies, suggesting rapid changes in the dense gas conditions during the merger. We compare the total stellar mass in clusters to the SFR of the galaxy, finding that these systems are among the most efficient environments to form star clusters in the local Universe.