[en] The triaxial superdeformed (TSD) rotational states in the odd-odd "1"6"0"-"1"6"8Lu isotopes are investigated by per-forming the configuration dependent three dimensional total Routhian surface (TRS) calculations with the explicit treatment of the deformation driving effects of the high-j intruder orbits. About fifty low lying TSD bands have been found for these odd-odd nuclei within the excitation energy of 3 MeV above the ND yrast bands. The configurations of calculated TSD bands have been assigned based on the TRS calculations and the analysis of q.p. energies in the rotating frame. The calculated equilibrium elongation and triaxial deformations for these TSD bands are close to ε_2 = 0.4 and γ = 200, respectively, which are the typical quadrupole deformations for the wobbling bands observed in the neighboring odd-even Lu isotopes. The detailed comparisons for the calculated TRS and the deformation driving effects of the intruder high-j orbits made between odd-odd Lu nuclei and the odd-even Lu wobbling nuclei result in the similar stability of the TSD shapes, indicating the possibility to observe the wobbling excitation in the former nuclei. However, the wobbling mode as an unique signature for the triaxiality has not been discovered in the odd-odd Lu isotopes, but observed in the neighboring nuclei "1"6"1","1"6"3","1"6"5","1"6"7Lu. We explain this puzzle based on the examination of the TSD band structure in odd-odd Lu isotopes, and found that the high level density at the second minimum in the TRS surface is the main reason for the difficulty to discover experimentally the wobbling bands in odd-odd Lu isotopes. (authors)