The electronic structure of the quasi-two-dimensional disk-like artificial atom involving holes inside has been studied by the full configuration interaction (FCI) wave function employing mixed basis sets consisting of standard atomic orbitals and anisotropic Gaussian-type functions. The one-particle confinement potential for electrons has been modeled by a sum of an anisotropic harmonic-oscillator potential and attractive Coulomb potentials, the latter being responsible for the hole positive charges. The oscillator strengths from the ground state to a number of low-lying excited states have been calculated by the FCI energies and wave functions for different strength of the harmonic confinement ω. The results for two electrons with a hole at the center, namely, the He-like system, have shown accumulation of the oscillator strengths distributed among different dipole-allowed transitions in the excitation into the center-of-mass modes or the plasmon modes for increasing confinement strength ω. The system of two electrons with two impurity holes, namely, the H2-like system, has been also studied, which has shown a far more complicated trend of the oscillator strengths with respect to ω owing to the additional degree of freedom of the internuclear distance r. The observed trend has been rationalized on the basis of the nodal patterns in the molecular orbitals and in the electron density distributions.