very screwy fonts with various versions of MSWord (and with LibreOffice)

I'm seeing the indication of which font is being used (or, as you say, called for) in the dropdown at the extreme left-hand end of the toolbar.

I did Select All and Validate Font, as well as Look for Enabled Duplicates, and there seem to be no problems.

In my test document, under Word2011, font substitutions  are under Word->Preferences->Compatibility, and I see:

And when I open FontBooks, Times seems to be there (but not Lucida Sans), and Times New Roman is "off"; this seems backwards.  I am bewildered.

Word displays the expected font in the font dropdown. If that font is not installed, it silently substitutes another. None of your samples look like Lucida Sans, so I doubt you have it installed. The first sample looks like Copperplate Gothic, the second looks like Arial or Helvetica and the third is a monospaced font, perhaps Lucida Sans Typewriter.

Bob's tip about testing in Font Book is a good one.

The first question is: Where are you seeing the indication of which font is being used?

The font selector on the Home tab as well as the Format> Font dialog indicate which font is called for based on the formatting metrics specified in the document file. That doesn't necessarily mean that the same font is being used to display the text in the document when viewed on screen. There are a number of reasons why a different font might be substituted for the specified font & not all programs [or even different versions of the same program] necessarily make the same substitution if substitution is required. Have you gone to Format> Font Substitution to see what it indicates?

Several of the more common reasons for substitution are that the specified font either (a) is not installed or (b) is available but is corrupt or (c) more than one version of the font is installed or (d) the font no longer is supported based of its type. [Word is particularly fussy about font type & validity in order to provide more accurate typesetting replication.]

Have you used the macOS Font Book app to confirm that Geneva is installed & if so which version? Also, use Font Book to Validate your fonts & Resolve Duplicates.

Out of curiosity, what happens if you select some of the text, choose a different font, then apply Geneva again?

Yeah, the stuff with Lucida Sans and Copperplate seems right.

I think I can narrow my bewilderment down to this:

0. In FontBook, selected all fonts and did "Validate Font" and "Look for Enabled Duplicates", and then "Restore Standard Fonts".
1. Created a test file, with one word which I tried to make Times format, using Format->Font and typing in "Times".   
2. With test file still open, in Format->Font in the scrollable menu of possible fonts, plain "Times" is not there (although Times Bold, Times Italic, Times Roman etc are).

3.. With that file still open, do Word->Preferences->Compatibility->FontSubstitution and there's an entry for "Missing Document Font" = "Times" and "Substituted font" = "Times Roman" (which is unsurprising, since it doesn't seem to think Times is there).

So since FontBook thinks Times is there, why does MSWord2011 think it is not ?

I believe the problem may be that Times (regular) and Times Roman are apparently synonymous.    Some of documents seem to think their font should be "Times" and MSWord is saying "no such thing" and substituting in "Times Roman" - which is the SAME thing.   Perhaps I created some of these documents in an older version of MSWord (Office X ?) that called it plain "Times" and that is the problem ?   That still doesn't explain how I ended up with some sections in the "Lucida Sans" font ...

Further complication arises from the fact that fonts seem to exist in (at least) three locations: /System/Library/Fonts, /Library/Fonts, and ~/Library/Fonts.   In FontBook->Preferences, you can select the second or third as the default install location (by selecting "Computer" or "User").   BUT, if you click the question-mark, you learn that "system fonts you download from Apple aren’t installed in these locations"; it appears that they are installed into /System/Library/Fonts.

I believe my problem is resolved, going forward at least.   It's still a bit of a puzzler why some of my documents seem to have a font called just "Times" (as opposed to "Times Roman").   And a complete mystery why some of my documents have "Lucida Sans" (I've never heard of such a font, and can't imagine why I'd use it if I had).

Font substitutions only occur when the Missing font is not installed. So my assumption was correct that Lucida Sans is not installed. The dialog also explains the appearance of Copperplate Light in your first screen shot.

I'm not clear why you're bewildered, please tell us more.