The electroacoustic resonances commonly known as Tonks-Dattner resonances were excited in neon, argon, xenon and mercury afterglow plasmas using microwaves in the frequency range 2 to 4 GHz. The afterglow plasmas were produced by high voltage dc pulses across electrodes in cylindrical discharge tubes located in S-band waveguides. Peak electron densities are measured utilizing the electroacoustic resonances. These are compared with those measured simultaneously using the microwave cavity perturbation technique. The nonlinear interaction of the transverse electromagnetic waves with the inhomogeneous plasma is probed as the excitation signal strength is increased from microwatts to hundreds of milliwatts. The second harmonic amplitude of the signal emitted from the plasma column when excited at plasma resonance is probed as a function of the excitation field strength and also as the gas pressure is varied. (Author Modified Abstract).