For Opera, or any application that may be buried in an unknown location, there are several ways to locate the application files, including spotlight searches and some terminal commands; however, in the case of applications that will open with contextual menu shortcuts, the simplest way to do this is the following:
Launch the Opera browser (or other application) using the 'open with' submenu in the contextual menus. The browser should display in the Dock as a normal application would.
Right-click the application and select the "Show in Finder" menu item. This will open a folder containing the browser.
Remove the application by deleting it.
Repeat this as long as the application can be located in the Finder in this way (users may have to restart their computers after each deletion to update contextual menus and other application links).
Here's a detailed tutorial about how to do clean and complete uninstall of Opera Mac.