Why would a 2013 iMac i5 with 16GB RAM suddenly run extremely slow after upgrading to Mojave 10.14.6

Try booting into Safe mode

http://support.apple.com/kb/ht1564

This will not load any 3rd party additions, it will load some more conservative Apple drivers (may cause screen flicker), and it will clear some kernel caches (a cache is saved data in a form that can speed up a program, but is totally redundant to the original source, and thus can be safely cleared).  Booting into Safe mode is just an experiment, but can frequently eliminate any 3rd party interference, or a cached item out-of-sync with the world.  (Verify Safe mode via Applications -> Utilities -> System Information -> Software -> Boot Mode -> Safe vs Normal)

Also please provided the EtreCheck, D.I. Johnson, requested.

Hello.

Sorry to hear you’re having this problem with your Mac.

You say your 1TB drive has only 108GB free. That may be part of your issue.

I think we can help you, but we’ll need a little bit more information about the computer

EtreCheck is an awesome little app that displays important diagnostic and debugging information about your Macintosh and allows you to copy that information to the Clipboard. It is very highly regarded and meant to be used with Apple Support Communities to help others help you with your Mac.

Please navigate to the Mac App Store and download the free version of EtreCheck OR please click EtreCheck.com where you will also find the app. Once you’ve downloaded the app and created the report please post it with your reply to this message. 

For instructions on how to download your EtreCheck report and attach it to your reply to this message, please click  How to use Add Text when posting…

We can then use the EtreCheck report to look for obvious issues that may be causing your problem and advise how to correct them.

d.i.