op amp oscillation problem during chip measurement
Try removing the capacitive load as a first step. Capacitive load will create a pole in the feedback loop in combination with the amplifier output resistance which will degrade the phase margin.  Also ensure input signals don't contain the ringing at the same time you are probing the output lines.  Check supply bypassing and stray inductance in feedback path.  Try adding feedback capacitance to roll off higher frequency amplifier gain (although the 20kHz ringing is unfortunately in band if your device is for audio).