We present a multi-wavelength investigation of the radio galaxy population in the galaxy cluster MOO J1506+5137 at $z$=1.09$pm$0.03, which in previous work we identified as having multiple complex radio sources. The combined dataset used in this work includes data from the Low-Frequency Array Two-metre Sky Survey (LoTSS), NSFs Karl G. Jansky Very Large Array (VLA), the Robert C. Byrd Green Bank Telescope (GBT), the Spitzer Space Telescope, and the Dark Energy Camera Legacy Survey (DECaLS). We find that there are five radio sources which are all located within 500 kpc ($sim$1$^{prime}$) of the cluster center and have radio luminosities $P_{mathrm{1.4GHz}}$ > 1.6$times$10$^{24}$ W Hz$^{-1}$. The typical host galaxies are among the highest stellar mass galaxies in the cluster. The exceptional radio activity among the massive galaxy population appears to be linked to the dynamical state of the cluster. The galaxy distribution suggests an ongoing merger, with a subgroup found to the northwest of the main cluster. Further, two of the five sources are classified as bent-tail sources with one being a potential wide-angle tail (WAT)/hybrid morphology radio source (HyMoRS) indicating a dynamic environment. The cluster also lies in a region of the mass-richness plane occupied by other merging clusters in the Massive and Distant Clusters of WISE Survey (MaDCoWS). The data suggest that during the merger phase radio activity can be dramatically enhanced, which would contribute to the observed trend of increased radio activity in clusters with increasing redshift.