You may need to close other audio-using programs before running Wine, particularly Firefox if you have any flash videos (youtube, etc) open. PulseAudio's Alsa compatibility layer does not like Wine very much, and sometimes the audio system breaks entirely when Wine uses it.
I also find it helpful to set my IM status to away so that the IM client doesn't create sounds while I'm running one of these applications.
You may also need to run killall -9 pulseaudio in a terminal once the audio has gotten off and Wine has exited. This will forcekill PulseAudio, which will then restart itself in a couple seconds.
The long term solution to this problem is to improve either Wine or PulseAudio. The PulseAudio developers have been pretty clear that they don't want to support Wine's "abuses" of the ALSA API, so the only solution for Wine is to stop using ALSA and instead have a PulseAudio output path for audio. You can read more about this here: http://yokozar.org/blog/archives/178 -- as far as time goes, Wine's OpenAL layer (and therefore PulseAudio support) is being actively worked on by two developers but I don't know when it will enter the code.