© 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. We have carried out multiwavelength observations of the nearby (z = 0.046) rich, merging galaxy cluster Abell 3376 with the Murchison Widefield Array (MWA). As a part of the GaLactic and Extragalactic All-sky MWA Survey, this cluster was observed at 88, 118, 154, 188, and 215 MHz. The known radio relics, towards the eastern and western peripheries of the cluster, were detected at all the frequencies. The relics, with a linear extent of ~1 Mpc each, are separated by ~2 Mpc. Combining the current observations with those in the literature, we have obtained the spectra of these relics over the frequency range 80-1400 MHz. The spectra follow power laws, with α =-1.17 ± 0.06 and-1.37 ± 0.08 for the west and east relics, respectively (S∝vα). Assuming the break frequency to be near the lower end of the spectrum we estimate the age of the relics to be ~0.4 Gyr. No diffuse radio emission from the central regions of the cluster (halo) was detected. The upper limit on the radio power of any possible halo that might be present in the cluster is a factor of 35 lower than that expected from the radio power and X-ray luminosity correlation for cluster haloes. From this we conclude that the cluster halo is very extended (>500 kpc) and/or most of the radio emission from the halo has decayed. The current limit on the halo radio power is a factor of 10 lower than the existing upper limits with possible implications for models of halo formation.