Three new highly-deformed (HD) bands are identified in 136Nd and the highly deformed band of 137Nd is extended at higher spin by four transitions, revealing a band crossing associated with the occupation of the second νi13/2 intruder orbital. Extended cranked Nilsson-Strutinsky calculations are performed for all HD bands observed in 134Nd, 136Nd, and 137Nd, achieving for the first time a consistent interpretation of all HD bands in the Nd nuclei. The new interpretation has significant consequences, like the change of parity of the yrast HD bands of 134Nd and 136Nd, and the involvement of two negative-parity neutron intruder orbitals in the configurations of most HD bands. The present experimental results and their theoretical interpretation represent an important step forward in the understanding of the second-minimum excitations in the Nd nuclei.