An algebraic model with three-body boson interactions is proposed to incorporate the different quadrupole modes in nuclear collectivity. It is shown that the recently observed anomalous collective structure characterized by B-4/2 = B(E2;4(1 )-> 2(1))/B(E2;2(1 )-> 0(1)) < 1.0 and R-4/2 = E(4(1))/E(2(1)) >= 2.0, which cannot yet be explained by any other microscopic nuclear models, naturally emerges in the present model due to the inclusion of triaxial rotor modes. This description is further extended to describe odd-A nuclei by including the coupling to the Fermion degree of freedom. This allows us to give a unified explanation of the anomalous B(E2)strengths in both even-even and even-odd systems, which indicate different behaviors. As examples, the model is applied to describe the spectroscopy and E2 transition properties of Os-168,Os-169,Os-170,Os-171. All recent measurements of these isotopes can be well reproduced on the same footing, which suggests that the anomalous collectivity persists even in odd-A systems.