Quick launch area: right click and choose remove. You don't uninstall the program, but it won't be in the quick launch area anymore and startup of Windows might be a little bit faster.
Systray is more complicated. A program running can decide to put itself in the system tray, or not. For some programs the only way to get them out of the system tray is to uninstall them, or - at least - not have them running at start up. Others have a properties sheet in the click or right click choices, or in the Options if run them normally, where you can choose to have them in the systray or not. Volume control (speaker icon) can be put on and off in Control Panel>Multimedia.
So no general clear-cut way to do it. Depends on the program.
Hope this helps.
I know there is a simple way to remove (uncheck boxes)quick launch icons from the systems tray and task bar but have forgotton how to do it. Will someone please forward me the instructions. Trying to clean up computer.