Ich verleihe kein Geld, das zerstört ja nur Freundschaften.
All three interpretations (a b c) that you give for the English version are also possible for the German version. There's no good way to know which one is meant except looking for the most semantically probable. If it's spoken, you can listen to the emphasis for a clue.
You're right of course about the general rule that "nur" normally comes before the thing that it refers to, but in this case having the "ja nur" together seems natural, so this is just the natural position for the "nur" in the sentence.
Your second idea:
Ich verleihe kein Geld, das zerstört ja Freundschaften nur.
... is actually a perfect way to put it and much clearer than the first one, because it limits the possible meaning to (b). The only slightly "unnatural" thing about it is that ja and nur are separated, but that's fine, you can definitely say or write that.
You could also say (with the same meaning):
Ich verleihe kein Geld, das zerstört Freundschaften ja nur.
Your third variation:
Ich verleihe kein Geld, nur zerstört ja das Freundschaften.
doesn't work, because the "nur" gets a whole different meaning when you put it in the beginning. It then becomes a conjunction then with the meaning of "though", which totally changes the relation between the sentences. In this case you're basically saying that NOTyou're not lending money although that (= not lending money) destroys friendships.
If you want be more explicit and use "weil", you can say:
Ich verleihe kein Geld, weil das ja nur Freundschaften zerstört. (= meanings a or c )
or
Ich verleihe kein Geld, weil das Freundschaften ja nur zerstört. (= meaning b)
or
Ich verleihe kein Geld, weil das ja Freundschaften nur zerstört. (= meaning b, the ja is a bit more emphasized)
I think it isn't possible so say it in a way that can only mean (c) withount making it longer, like
Ich verleihe kein Geld, weil das nur eins bewirkt, nämlich Freundschaften zu zerstören.
My general rule for the position of the "ja" would be to put the "ja" (or other Modalpartikel) just before other adverbs like "nur". You can place an object between them if you want, but the Modalpartikel always comes first.