Apparently the phrase “Sehr Gerne” means different things depending on your name !?
Can anyone explain this … er … weirdness ?
The explanation is easy: only the first translation is exactly correct (“You’re welcome”), and Google translation sucks.
The only other translations that make sense are “Very happy to, Sue” or “I’d love to, Pete”, which are possible anwers if the preceding question was “Kannst du mir helfen?” (“Can you help me?”).
Evidently, Google “translated” your phrases by cutting and pasting from random texts that correspond to the context, simple as that. It does not “understand” that gerne means “You’re welcome” or anything else.
What @DPRK said is exactly how Google Translate works. It’s trained on texts that have been translated by humans, e.g. a document that has both an English version and a German version.
This method was found to be a lot more accurate than the previous version where they would try to just program in a dictionary, as this would often result in the wrong definition of a word being used.
The “holy grail” of actually parsing language for meaning and then translating that meaning (i.e. what humans translators do) has not been achieved in software.
That holy grail has not been achieved, that is true, but they are much closer than I ever thoght possible. But it is not Google, it is Deepl.com who leads IMO. And still there are issues with your query:
Sehr Gerne is wrong. Gerne is not capitalized. Capitalizing “gerne” turns it into a substantive that does not exist. And you should insert a comma between gerne and the name. Try it then, writing the German sentence correctly, and see what happens. Deepl has problems with “Sehr gerne” but does fine with “Sehr gerne, XXX”, XXX being any name.
Google translate is generally pretty bad, but how bad depends on the language. Translating Hungarian to English is barely comprehensible. Translating Japanese to English usually results in gibberish.
As I wrote, Deepl is much better, but it admittedly has much less language pair combinations than Google.
Of course computers have a hard time with erroneous sentences to start with, while humans can think what the sentence was meant to be (as I just did: speculation, but probably right). Computers never get tired, but get stuck in a rut. They are mechanical/probabilistic, humans are heuristic.
Slightly better :
I’d say that’s more than slightly better. The only variation is just a different wording for the exact same thing. So your list no longer includes any mistranslations.
Sligtly? That is good. Good enough anyway. I would not have done it much better (well… context can change everthing, but hey! Computers don’t know of any context that is not explicitly stated - and when a human assumes too much context, they may be soooo wrong) and I am a profesional interpreter.
Of course the sentence was very simple.
PS: Have you noticed that the difference between your first three sentences and the fourth is that Sue is female? Perhaps I am interpreting (ha! my job! literally) too much into what Google assumes, but it gets more polite (for lack of a better word, English is not my first language, but perhaps you feel it too) when a woman is the subject. Do you have a different explanation? I may well be wrong.
Problem solved?
No !
(But the question has been answered !)
Now I wonder what the problem was.
Ok, here’s the story :
Using Google Translate (GT), I sent a message to a German company
asking if they deliver to the UK.
A nice lady sent back a replay saying they do, and “Liebe Grüße”.
I replied “Dankeschön, und liebe Grüße auch an dich”
She replied “Sehr gerne PJD”…
When I translated this, i got “I’d love to PJD” !
OMG ! What did I propose ?!
Now a bit of playing with GT led me to believe everything
was innocent, but there’s clearly potential for confusion
or embarrassment, or comedy.
Anyway, in future i’ll just remember EinsteinsHund’s conjecture that GT sucks.
This sort of thing always brings comfort whenever i hear that “robots are
going to take over the world”. That and the fact they’re not even smart enough to
click a box that says “i am not a robot”.
?
You thanked her, and she replied, “You’re [very] welcome”.
Yes, i know.
But when she said “You’re very welcome”, GT told me she’d said “I’d love to”
Which could cause confusion etc.
If you want to test how good a translation programm is, I recomend a simple test: Take any text, copy and paste it. A newspaper article will do. Let the machine translate it into, say, French. Translate the translation into German. Translate this translation into Russian. Repeat with as many languages as you fancy. Finally, let the machine translate the text back into English. Compare the original with the translation. How much do you understand?
You will see that some laguages get better translated (French to Italian, Italian to Spanish), others are more difficult (German, Russian) and others are incomprehensible (Hungarian, Turkish, Japanese, Chinese). That is due in part to the structure of the languages (Italian, Spanish and French are pretty parallel, German is syntactically difficult, but Google can handle this, Hungarian is grammatically complex, Google folds) and in part due to the process of training the programms. As DPKR and BigT have noted, Google “learns” by comparing the work done by others (they are stealing, BTW!) in a big database. For some languages (Hungarian and, curiously enough, Chinese) the database is much smaller.
As I said before, those programms are not really good, professionals have much higher standards (and we still make mistakes, of course). But they are much better already than I thought would be possible. You must know their limits and what they can be safely used for.
Just to show what translation can be, how weird translators think and how complicated they reason when they look at a simple sentence I would like to share this link with you:
That all about a four word sentence! (But not any sentence: “Aujourd’hui, maman est morte.”)
If you read that article, you will understand that I correct you, I can’t avoid it:
Next time, write Dich with a capital “d”. It shows more respect. Or Ihnen, (siezen vs duzen like in French vous vs tu, in Spanish usted vs tu… this formality does not exist in English, just believe me) which is really respectful. You commited no faux-pas, don’t worry, just a wee bit too informal.
Actually, the brief conversation was very informal from the first response,
namely :
"Hey PJD 
Danke für deine Nachricht.
Ja, wir versenden auch nach Großbritannien!
Liebe Grüße "
That is something a translator should take into account, I did not know this: your answer was perfectly fine. Much the better. Please bear with my nitpicking, as I said, translators can be weird with details. Interpreters are much cooler 
I’d point out that computers translators also tend to do better with more context. The “copying and pasting” mentioned above is based on heuristics, choosing based on how well the input matches what is in the database. The more context, the better the chance it matches with the correct one.
I also note that, unless things have changed with Google Translate, you can click on the translation and see other possible translations of that part of the sentence. I’ve found this quite helpful.