Since I only find a Windows version on that site, I assume you used wine to install it. You can try to use the wine uninstaller, by running (in a terminal emulator or in the run-dialogue - ALT+F2)
That should bring up a dialogue similar to the one used uninstall software in older versions of Windows. You should be able to uninstall the program that way. This will probably not remove the icons from the menus though, nevertheless they should stop working after uninstalling direcdownloader. For me, to remove the icons, it was enough to try to start direct downloader after uninstalling it. If that doesn't work for you, you can remove them manually. You can either use a program named alacarte (in the menus it's listed as Gnome-Main-Menu or something like that, if it's not installed, you can find it in software center by searching for alacarte.), or navigate to the hidden folder .local/share/applications in your home-directory and look for files named wine-Programs-DirectDownloader-DirectDownloader.desktop or similar and check the wine subdirectory.
If this however does not work for you and you are certain that you used wine to install directdownloader, you can try to delete all installed windows programs by deleting the hidden .wine-folder in you home directory. As said, this will remove all windows programs, so I'd only consider it a last resort, as long as any other windows-software additional to directdownloader is installed. Also, this will not remove the icons from the menus, you'll have to delete them manually (see above).
I must confess that I only tried this partially, for I'm not using the default desktop and therefore don't know how exactly it affects Ubuntu. If it also puts itself in autostart, the default directory for this would be the hidden .config/autostart-folder in your home directory.