Using the Einstein, Bergmann-Thomson (BT) and Landau-Lifshitz (LL) energy and momentum formulations in teleparallel gravity (TG), we obtain the total energy and momentum distributions for phantom black hole metric. We get different energy distributions similar to the earlier study and the momentum distributions vanish for phantom black hole metric in TG. These momentum solutions agree with the study of Sahoo et al. in general relativity. However, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy and momentum complexes, we investigate regular black hole, asymptotically flat wormhole, anti-de Sitter wormhole and Ellis wormhole solutions in TG. We obtain i) same BT and LL energy density solutions for regular black hole metric, (ii) same and zero energy distribution for asymptotically flat wormhole, (iii) proportion with Einstein and BT energy density solutions for anti-de Sitter wormhole, (iv) same and negative Einstein and BT energy density solutions for Ellis wormhole in TG.