Several new bands have been identified in $^{130}$Ba, among which there is one with band-head spin $8^{+}$. Its properties are in agreement with the Fermi-aligned $\nu h_{11/2}^2$, $7/2^{-}\left[523\right]\otimes 9/2^{-}\left[514\right]$ Nilsson configuration. This is the first observation of a two-quasiparticle t-band in the $A=130$ mass region. The t-band is fed by a dipole band involving two additional $h_{11/2}$ protons. The odd-spin partners of the proton and neutron S-bands and the ground-state band at high spins are also newly identified. The observed bands are discussed using several theoretical models, total Routhians surfaces (TRS), tilted axis cranking (TAC), particle rotor model (PRM) and projected shell model (PSM), which strongly suggest the coexistence of prolate and oblate shapes polarized by rotation aligned two-proton and two-neutron configurations, as well as prolate collective rotations around axes with different orientations. With the new results, $^{130}$Ba presents one of the best and most complete sets of collective excitations that a γ-soft nucleus can manifest at medium and high spins, revealing a diversity of shapes and rotations for the nuclei in the $A=130$ mass region.