We present the analysis of our 13 and 22 cm ATCA observations of the central region of the merging galaxy cluster A3921 (z=0.094). We investigated the effects of the major merger between two sub-clusters on the star formation (SF) and radio emission properties of the confirmed cluster members. The origin of SF and the nature of radio emission in cluster galaxies was investigated by comparing their radio, optical and X-ray properties. We also compared the radio source counts and the percentage of detected radio galaxies with literature data. We detected 17 radio sources above the flux density limit of 0.25 mJy/beam in the central field of A3921, among which 7 are cluster members. 9 galaxies with star-forming optical spectra were observed in the collision region of the merging sub-clusters. They were not detected at radio wavelengths, giving upper limits for their star formation rate significantly lower than those typically found in late-type, field galaxies. Most of these star-forming objects are therefore really located in the high density part of the cluster, and they are not infalling field objects seen in projection at the cluster centre. Their SF episode is probably related to the cluster collision that we observe in its very central phase. None of the galaxies with post-starburst optical spectra was detected down our 2$sigma$ flux density limit, confirming that they are post-starburst and not dusty star-forming objects. We finally detected a narrow-angle tail (NAT) source associated with the second brightest cluster galaxy (BG2), whose diffuse component is a partly detached pair of tails from an earlier period of activity of the BG2 galaxy.