RE: Erase History doesn't do what you hope
Both history (sites you've visited) and typed addresses (things you've typed into the address bar) are removed when you click Opera -> Clear Browsing Data... and select an appropriate time range at the top (by default it removes accesses from the last hour).
If you have visited a site, it would appear that Opera remembers it in terms of the autocomplete function. Even uninstalling and reinstalling from scratch doesn't make it forget.
As with other applications on Mac, Opera has a profile directory, which doesn't get removed when you remove the application itself. You can find it in $HOME/Library/Application Support/com.operasoftware.Opera, and you're free to remove it. This will remove all data that Opera has saved.
And if you want to remember later where to find it, the directory is also listed in Opera's about screen, which you can access using Opera -> About Opera.