Outlook hacked

Exactly. It's an attempt to get money...  actually had one guy say he was going to pay, even after I said the email was a lie... because he visited "naughty" web sites and didn't want his friends to know. {sigh}

Hacker claims a trojan virus is on my phone which is invisible to antivirus software. No idea whether this is complete nonsense. 

That is nonsense - they want to scare the user into paying.  This is my article when my account received a similar message: No, you're not being blackmailed  

The attempts to get in are unrelated to that message - the address was exposed in a database breech and all the bad actors are seeing if they can get in.  

One option if you have a lot of sign in attempts in the activity list at https://account.live.com/Activity :   
1. Add a new alias, set it as primary then remove sign in permission from the current address  

2. Add an alias here - https://account.live.com/names/manage   
DO NOT REMOVE THE CURRENT ADDRESS!   If you do, it is gone forever. You only want to add a new alias and set it as primary.  

3. Change sign in preferences using the link at the bottom of that page -  https://account.live.com/SignInPreferences     

When you sign in, you need to use the new alias. Do not use the alias anywhere else - only for logging in so it won't get exposed in a data breech.   

I have screenshots in this article: https://www.outlook-tips.net/tips/keeping-hackers-microsoft-accounts/