The localized excitations in the competing bond-order-wave(BOW), charge-density-wave(CDW), and spin-density-wave(SDW) systems are investigated within the Bogoliubov-de Gennes formalism using an extended Peierls-Hubbard model. An extensive study of localized excitations over a wide range of the on-site e-ph coupling lambda(2) and the Hubbard interaction U leads to the following observations : (a) As lambda(2) increases at fixed U, the number of bound states inside the gap changes from two to four for the STE case and from two to three for the polaron case. (b) A non-monotonic dependence of the lattice relaxation energy on lambda(2) is predicted within the lattice relaxation approach developed by two of us earlier, and is attributed to a crossover from the weak-coupling to strong-coupling behavior showing up as the emergence of new bound states inside the gap. Moreover, the non-radiative transition rate of STE is also calculated and is used to tentatively interpret the very short life-time of STE in PtCl complexes.