We have performed 323 MHz observations with the Giant Metrewave Radio Telescope of the most promising candidates selected from the MACS catalogue. The aim of the work is to extend our knowledge of the radio halo and relic populations to z > 0.3, the epoch in which massive clusters are formed. In MACSJ1149.5+2223 and MACSJ1752.1+4440, we discovered two double-relic systems with a radio halo, and in MACSJ0553.4−3342 we found a radio halo. Archival Very Large Array observations and Westerbork Synthesis Radio Telescope observations have been used to study the polarization and spectral-index properties. The radio halo in MACSJ1149.5+2223 has the steepest spectrum ever found so far in these objects (α ≥ 2). The double relics in MACSJ1149.5+2223 are peculiar in their position that is misaligned with the main merger axis. The relics are polarized up to 30 and 40 per cent in MACSJ1149.5+2223 and MACSJ1752.040+44, respectively. In both cases, the magnetic field is roughly aligned with the relics’ main axes. The spectra in the relics in MACSJ1752.040+44 steepen towards the cluster centre, in agreement with model expectations. X-ray data on MACSJ0553.4−3342 suggest that this cluster is undergoing a major merger, with the merger axis close to the plane of the sky. The cores of the disrupted clusters have just passed each other, but no radio relic is detected in this system. If turbulence is responsible for the radio emission, we argue that it must develop before the core passage. A comparison of double-relic plus halo system with cosmological simulations allows a simultaneous estimate of the acceleration efficiencies at shocks (to produce relics) and of turbulence (to produce the halo).