Your Sound cards are detected and listed ok and everything looks to be configured ok too. aplay -l outputs;
dcerouter_31437:~# aplay -l
**** List of PLAYBACK Hardware Devices ****
card 0: NVidia [HDA NVidia], device 3: HDMI 0 [HDMI 0]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: NVidia [HDA NVidia], device 7: HDMI 0 [HDMI 0]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: NVidia [HDA NVidia], device 8: HDMI 0 [HDMI 0]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: NVidia [HDA NVidia], device 9: HDMI 0 [HDMI 0]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 1: Set [USB Headphone Set], device 0: USB Audio [USB Audio]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 2: Set_1 [USB Headphone Set], device 0: USB Audio [USB Audio]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 3: Set_2 [USB Headphone Set], device 0: USB Audio [USB Audio]
Subdevices: 1/1
Subdevice #0: subdevice #0
But as soon as a squeezeslave starts up it dies. Which makes me think Squeezeslave is not happy with your USB sound card. Have you had these sound cards working before? Do you have a different card to use as a test of that theory?
All the best
Andrew