In a companion work (Contreras Pena et al., 2017MNRAS.465.3011C, Paper I), we detected a large population of highly variable Young Stellar Objects (YSOs) in the Vista Variables in the Via Lactea (VVV) survey, typically with class I or flat spectrum spectral energy distributions and diverse light-curve types. Here we present infrared spectra (0.9-2.5 {mu}m) of 37 of these variables, many of them observed in a bright state. The spectra confirm that 15/18 sources with eruptive light curves have signatures of a high accretion rate, either showing EXor-like emission features ({Delta}v=2 CO, Br{gamma}) and/or FUor-like features ({Delta}v=2 CO and H_2_O strongly in absorption). Similar features were seen in some long-term periodic YSOs and faders but not in dippers or short-term variables. The sample includes some dusty Mira variables (typically distinguished by smooth Mira-like light curves), two cataclysmic variables and a carbon star. In total, we have added 19 new objects to the broad class of eruptive variable YSOs with episodic accretion. Eruptive variable YSOs in our sample that were observed at bright states show higher accretion luminosities than the rest of the sample. Most of the eruptive variables differ from the established FUor and EXor subclasses, showing intermediate outburst durations and a mixture of their spectroscopic characteristics. This is in line with a small number of other recent discoveries. Since these previously atypical objects are now the majority amongst embedded members of the class, we propose a new classification for them as MNors. This term (pronounced emnor) follows V1647 Ori, the illuminating star of McNeil's Nebula.