If you have no use whatsoever for the app then just delete it from your Applications folder.
First look in Activity Monitor
(Applications ~> Utilities) and set the pull-down menu in the upper right to:
"All Processes, Hierarchically".
See that there is nothing that is running that belongs to Entourage, if there is something you can highlight it and click on
"Force Quit" in the menu of the Activity Monitor Window.
Then go the your Applications folder and find Entourage, then drag it to the Trash and empty it.
I can't say as I never use this app, but it might be a part of a larger Microsoft Application Suite that you have installed .... I don't know for certain and if you can't see it in the Applications folder, then try a Spotlight search for it .... Command () + Spacebar will activate the Spotlight text box in the upper right of your screen and just type Entourage and see what surfaces.
Might be worth looking at the Entourage icon next time it appears in the Dock. Click on the icon and check in the contextual menu to see if
"Open At Login" is selected.
You can also check:
System Preferences ~> Accounts ~> Your Account ~> Login Items Tab
You might need to unlock the Padlock with an Admin name/password to proceed and Entourage may/may not be in the list .... FWIW, the tick box to the left of an item just denotes whether the item is hidden or not, or running in the background if you like. So if it's there, just select it and click on the minus sign (-) below, to remove it.
Please let me know how you get on with this and don't let it bug you ... things could be worse ... a whopping scary T-Rex could be picking up your scent