Résumé : We report on mass measurements of three long-lived states in 114Rh performed with the JYFLTRAP Penning-trap mass spectrometer: the ground state and two isomers with estimated half-lives of about one second. The used Phase-Imaging Ion-Cyclotron-Resonance technique allowed for the discovery of a so far unknown second long-lived isomer. All three states were produced directly in proton-induced fission on a uranium target, whereas only the isomeric states were populated in the β decay of the 114Ru ground state with spin-parity 0+. We propose spin-parity assignments of (6−) for the ground state, and (3+) and (0−) for the isomers. They resolve the puzzle of anomalous fission yields of this isotope despite the existing literature assigning a low angular momentum to the ground state. The experimental evidence is further supported by a detailed analysis based on mean-field calculations with the BSkG3 model. As for many other nuclei in this mass region, considering triaxial shapes is decisive for the interpretation of low-lying states of this nucleus. The discovery of a new isomer in 114Rh and our theoretical work challenge the currently adopted spin-parity assignments in this and several other odd-odd neutron-rich Rh isotopes.