MOUSE (philips mouse plugged into iMAC usb hub) and KEYBOARD (apple keyboard) gone wild. MAC OS is 13.4.1

First, there is no reason to ever install or run any 3rd party "cleaning", "optimizing", "speed-up", anti-virus, VPN or security apps on your Mac.  This documents describe what you need to know and do in order to protect your Mac: Effective defenses against malware and other threats - Apple Community and Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support.  

There are no known viruses, i.e. self propagating, for Macs.  There are, however, adware and malware which require the user to install although unwittingly most of the time thru sneaky links, etc.   

Anti Virus developers try to group all types as viruses into their ad campaigns of fear.  They do a poor job of the detecting and isolating the adware and malware.  Since there are no viruses these apps use up a lot of system resources searching for what is non-existent and adversely affect system and app performance.

There is one app, Malwarebytes, which was developed by a long time contributor to these forums and a highly respected member of the computer security community, that is designed solely to seek out adware and known malware and remove it.  The free version is more than adequate for most users.  

Also, unless you're using a true VPN tunnel, such as between you and your employer's, school's or bank's servers, they provide false security from a privacy standpoint. 

Uninstall irus Protection Scan according to the developer's instructions. Do the same for any apps that fall in to the other categories.

Try the Apple supplied mouse and keyboard. If they work successfully, they tends to eliminate the cause being the iMac itself.

Have you tried non Apple KB and mouse on a different Mac? Either iMac or MacBook Pro or Air.

Your call. But it sounds like your mouse is physically damaged to me; maybe the same for the KB.