Remove Search.strtpoint.com Search Engine
I think I have solved my problem.

I got an exception from Safari which suggested "External Modification Warnings: Thread creation by external task."

I found many references on the web (most for Windows) and some suggesting going to Safari\Preferences\Extensions and turning off. I wasn't even going to try those which suggested I install yet another app from the web.

Seeing as I could not even start Safari the above was not useful. I could start Safari in Safe mode, but there was nothing there - possibly because when it originally wanted access to all my private data I refused. 

Activity Monitor showed an Installer and this had ~/Library/Application Support/com.genieoinnovation.Installer/Completer.app/Contents/MacOS/Installer open.
I deleted this directory. Unfortunately this did not fix the problem.

I tried @Buscar웃 suggestion, but this only found references to old preferences in Firefox and Chrome, which I had already fixed.

I then tried sudo mdfind com.genieoinnovation and found the following.

/Library/LaunchDaemons/com.genieoinnovation.macextension.client.plist
/Library/PrivilegedHelperTools/com.genieoinnovation.macextension.client
/Library/Frameworks/GenieoExtra.framework/Contents/Library/LaunchServices/com.genieoinnovation.macextension.client
/Library/Frameworks/GenieoExtra.framework/Contents/Resources/en.lproj/com.genieoinnovation.macextension.plist
/Library/LaunchAgents/com.genieoinnovation.macextension.plist

/Users/ian/Library/Application Support/com.genieoinnovation.Installer/Completer.app/Contents/MacOS/Installer


Deleting all these seems to have resolved the issue.