3d transition-metal oxide materials with strong electron correlations and low dimensionality give rise to emerging exotic phases. Resonant inelastic X-ray scattering (RIXS) has developed as a powerful spectroscopic tool for probing the collective excitations in such correlated materials. The RIXS technique provides an ideal approach for assessing electronic instabilities in condensed matter. This thesis comprises the experimental RIXS response of the spin chain-ladder cuprates Sr14-xCax(Cu,Co)24O41 and frustrated honeycomb nickelate Na2Ni2TeO6. The spin and charge excitations of Sr14-xCaxCu24O41 (x=0 & 12.2) are studied by Cu L3-edge RIXS. With increasing Ca content, a crossover from collective two-triplon excitations (x=0) to a damped incoherent magnetic spectrum ~280 meV (x=12.2) in the ladders is uncovered from the RIXS spectra, dominated by spin-flip ΔS=1 scattering. With model calculations, the localized broad magnetic mode at x=12.2 is shown to be a consequence of enhanced elecrtronic localization. This is supported by polarization-dependent measurements, where the evaluated non-spin-flip ΔS=0 scattering is showing weight depletion below 1 eV. The RIXS spectral evolution suggests that a suppressed carrier mobility dominates the low-energy physics in Ca-rich phases. The low-energy excitations of Sr14Cu24O41 are also studied by O K-edge RIXS at the upper Hubbard band. The RIXS spectra show a sharp dispersing peak of similar energies to the ΔS=1 two-triplon excitations, and a broad non-dispersive mode at higher-energy. By comparing the experimental results to the existing theories of doped ladders, the observed spectral modes are attributed to interacting holon-spinon quasiparticles, with additional spectral contributions from the ΔS=0 multi-triplon bound states and continuum. These observations highlight the RIXS capability for resolving composite spin-charge quasiparticles and long-lived ΔS=0 magnetic excitations, which are difficult to detect by other experiments. Charge order and phonons for the two-leg ladders of Sr14(Cu,Co)24O41 are studied. At the ladder hole peak in O K-edge XAS signal, a concomitant elastic enhancement and phonon-softening is observed across all Co doping levels. The in-plane diffraction and phonon-softening response are found to enhance with increasing Co doping. Morevoer, the observed diffraction signal is further characterized by energy- and temperature-dependent measurements. Lastly, given the strong electron-phonon coupling (EPC) observed in O K-edge RIXS spectra, the EPC strength can be analyzed from the RIXS intensity decay of the phonon overtones . The observed in-plane resonant diffraction and inelastic phonon response strongly suggest an enhanced stripe order via magnetic impurities, reminiscent of the reports in CuO4 plaquettes. Electronic structure and EPC of the honeycomb nickelate Na2Ni2TeO6 are studied. Compared with current literature, the localized excitations (1-4 eV) in the Ni L3-edge RIXS spectra are dominated by the crystal-field splitting of a Ni2+ ion in octahedral coordination. At the O K-edge, the large EPC ~285 meV with 5 recognizable overtones (frequency of ~80 meV) are revealed in the RIXS spectra. The observed modes provide a systematic characterization of charge, orbital and lattice dynamics for a newly proposed frustrated antiferromagnet. This thesis has been carried out in a collaboration between the Paul Scherrer Institut and the Laboratory for Quantum Magnetism at EPFL.