Well I'm not extremely familiar with Azureus, but here's one little bit I found that might help.
* Limit the Maximum # of connections per torrent in Configuration->Transfer to 30 or less.
Enable the Slowly connect new peer connections option, also in Configuration->Transfer.
NOTE: CVS versions 2105_B44 and newer employ new code that makes 'Slowly connect...' option obsolete. It is recommended you upgrade to the latest cvs version if you're having problems.
* Enable the Use alternative socket polling option, also in Configuration->Transfer.
Note: If you are running Zone Alarm (version 5 in particular), you might try disabling or uninstalling it and rebooting. Many users have reported problems with ZA breaking bittorrent clients.
# Uninstall ZoneAlarm 5.0 and use either a previous version or a different firewall application.
# Upgrade to the latest Java Runtime Environment (JRE) 1.50 beta. http://java.sun.com/....0/download.jsp
Let me know if any of this helps or not. If not, then we will look further into this.