Is there a way to disable the strong's number display that occurs upon mouse-over/hover?
This easiest way is to simply delete all your lexicons (at least the ones indexed by strongs).
The second easiest, is of course not to read anything that's showing strong's numbers. This is a little more complicated.
And finally, all else failing, is to not use Logos4.
I've no idea why Logos (Bob) loves popups SO MUCH. I bet the street he lives on has popups posted all along it (attached to the trees).
Actually there's a last solution and that is to use a touch computer (my solution).
There isn't a direct way to disable popups and deleting lexicons isn't practical as all of them also handle lemmas (including Vine's, Enhanced Strong's).