Plasmonics with subwavelength characteristics can break the diffraction limit of light and be used to produce the sub-wavelength optoelectronic device, thus it has aroused great interest for decades. Local surface plasmon resonance of metal nanoparticles has become one of the research hotspots due to the fact it can produce extinction and near-field enhancement effect. How to achieve controllable plasmon line shape and generate strong electromagnetic field enhancement is of great significance for improving the sensing performance, nonlinear effect and surface enhanced Raman factor of metallic nanostructures. The optical properties of plasmonic oligomer clusters composed of normal and L-shaped nanrod dimers are investigated by using the finite-difference time-domain method in this paper. There are two energy modes for an L-shaped nanorod due to its shaped anisotropy, where plasmons oscillate along the arms of the L-shaped nanorod or oscillate over the whole length of the L-shaped nanorod. Therefore, two bonding resonances appear in the spectrum of an L-shaped nanorod dimer, while only one bonding resonance exists for normal nanorod dimer. When a normal nanorod dimer and an L-shaped nanorod dimer are aligned together to form a quadrumer, the three bonding resonances can be excited simultaneously and radiative damping can be suppressed effectively around the dip spectral positions. It is shown that the optical responses of quadrumer can be strongly tuned by manipulating the geometry parameters. For example, the coupling between the two dimers can be modified by adjusting the separation, and the three resonances shift toward higher energies with the increasing of the separation. In addition, the optical responses of individual nanorod depend on the corresponding arm length. As a result, the three resonances of the quadrumer can also be well tuned by adjusting the arm length. Comparing the variation of resonance peak positions between L-shaped nanorod dimer and normal nanorod dimer, we can more intuitively understand spectral lineshape variation of quadrumer. These results can be used for guiding the design of nano-photonic devices for plasmonic oligomer clusters and also for developing the application of surface-enhanced Raman scattering and biological sensing.