High-spin terminating bands in heavy nuclei were first identified in nuclei around Er-158(90). While examples of terminating states have been identified in a number of erbium isotopes, almost nothing is known about the states lying beyond band termination. In the present work, the high-spin structure of Er-156,Er-157,Er-158 has been studied using the Gammasphere spectrometer. The subject of triaxial superdeformation and 'wobbling' modes in Lu nuclei has rightly attracted a great deal of attention. Very recently four strongly or superdeformed (SD) sequences have been observed in Hf-174, and cranking calculations using the Ultimate Cranker code predict that such structures may have significant triaxial deformation. We have performed two experiments in an attempt to verify the possible triaxial nature of these bands. A lifetime measurement was performed to confirm the large (and similar) deformation of the bands. In addition, a high-statistics, thin-target experiment took place to search for linking transitions between the SD bands, possible wobbling modes, and new SD band structures.