I am not sure about azeurus.
Most of the time you put manually installed packages in /usr/local/
/usr/local is usually reserved as a special place just for local admins so that when you update your OS or upgrade between version numbers it will always be left alone.
However Azuraus is originally a windows app, so it may not have the same preferences setup as normal linux applications. Normally you have a linux app and it stores it's preferences in a hidden file in the user's home directory. This is done because users have no or very little rights outside their home directory. In Windows however users have rights or don't have rights depending on the program and most of the time preferences are kept outside the home directory in a file called the registry.
So it may turn out that users have to have rights to the azuraus directory, in case it won't work because azuraus was designed as a single user aplication, unlike most Linux aps which are designed to be used in a Unix multiuser enviroment.
However if azuraus handles things correctly then you generally put it the azuarus in /usr/local/share
and put this script in /usr/local/bin
#! /usr/local/env bash
cd /usr/local/share/azureus
./azureus
and that should work. But I don't think it's that intellegent, being it's a mostly windows app.
But it'll probably just be easier to put a copy of azureus in each user's home folder. Most of the time you have a folder called /etc/skel
contents of that directory gets copied to a user's home directory when you use system scripts to create a new user. I'd make a directory called
/etc/skel/.apps
and copy the azureus folder to that.
then add a script to /usr/local/bin
#! /usr/bin/env bash
cd ~/etc/skel/.apps/azureus
./azureus
Then copy the folder to all existing users:
ls /home/ | while read i; do mkdir /home/"$i"/.apps; cp -r azureus /home/"$i"/.apps/azureus; done
And their you go.
If you don't want to do that or if that is too "non standard" then there are plenty of Linux specific bittorrent clients. It's a permissions issue. Lots of things that you can get away with in Windows, you can't get away with in Linux in a clean and safe fasion.