Alsa is the standard sound system with hardware support and PulseAudio is an additional system which can use Alsa devices.
PulseAudio is necessary for flash videos in firefox to play with sound and also my skype installation needed PulseAudio.
For volume control one can easily use amixer from Alsa. Most problems arose from wrong default devices selected by PulseAudio.
You can change those with the pacmd command and use the corresponding index.
The commands for pacmd are
list-sinks, list-sources, set-default-sink, set-default-source
where you can give the index of the propper Alsa device.
If timidity server is running in background it blocks Alsa on my system. I have to manually stop the timidity-daemon before I can access Alsa devices from other software.