This thesis describes the studies for two groups of molecules in the gas-phase: (a) copper monofluoride (CuF) and copper hydroxide (CuOH); (b) thorium monoxide (ThO) and tungsten carbide (WC). Copper-containing molecules (Group a) are selected to investigate the ionic bonding in transition metal-containing molecules because they have a relatively simple electronic state distribution due to the nearly filled 3d-orbital. ThO and WC (Group b) are in support of particle physics for the determination of electron electric dipole moment (eEDM), de, the existence of which indicates new physics beyond the Standard Model. The determination of the tiny eEDM requires large electric fields applied to the electron. The 3(Delta)1 states for heavy polar molecules were proposed [E. R. Meyer, J. L. Bohn, and M. P. Deskevich, Phys. Rev. A 73, 062108 (2006)] to determine de with the following attractive features: (1) large electric dipole moments; (2) large internal electric fields, Eeff, experienced by valence electrons; (3) nearly degenerate omega-doublets; (4) extremely small magnetic dipole moments. The H3(Delta)1 state for ThO and the X3(Delta)1 state for WC are both good candidates. Spectroscopic parameters (i.e. molecular electric and magnetic dipole moments, omega-doubling parameters, etc) are required for the 3(Delta)1 states of ThO and WC. High resolution optical spectra (linewidth ~50 MHz) of CuF, CuOH, ThO and WC were recorded field-free and in the presence of a static electric field (or magnetic field) using laser ablation source/supersonic expansion and laser induced fluorescence (LIF) detection. The spectra were modeled by a zero-field effective Hamiltonian operator and a Stark (or Zeeman) Hamiltonian operator with various molecular parameters. The determined molecular parameters are compared to theoretical predictions. The small omega-doubling parameter was well determined using the pump/probe microwave optical double resonance (PPMODR) technique with a much higher resolution (linewidth ~60 kHz) than optical spectroscopy. In addition to the above mentioned studies of the two groups of molecules, a resonance enhanced multi-photon ionization (REMPI) combined with a time-of-flight mass spectrometer (TOFMS) has been developed to identify the molecules responsible for observed LIF signals. The operation of this spectrometer has been tested by recording the mass spectrum of Ti/O2 and the REMPI spectrum for TiO using a two-color excitation scheme.