I'm going to assume that the rules for personal use are fairly obvious, but if someone wanted to make a set of artwork/actual cards for one of the entries from the Design-A-Villain contest that's posted in the forum, where (if anywhere) would it be OK to share those with others?
Board Game Geek has a Variants forum where things like that can be posted.
I'm aware of the Variants forum; the question is more in regards to the specific legal nature of the Villain Contest entries, as they're owned by GTG. That does seem like it would create a different set of issues than simply creating a villain and posting it there.
The design a villain contest is closed. I'm not sure I understand why you think submissions could still be made
HikariStarshine is not talking about "made" as in submitting-an-entry-to-the-contest but "made" as in taking-an-idea-from-the-contest-and-releasing-it-as-a-fan-expansion; with the standard boilerplate legal text that went along with submitting an entry to the contest HS is asking if it would be legally allowed or if >G would be all over them like cheese on Tachyon's pizza.
The answer is most probably, let's see what Paul and the others make of this request and see if they respond.
It wouldn't be >G, but their lawyers who would say one way or the other.
While it is likely safe, Lawyers might not agree, and smart businesses listen to their lawyers.
If you like the theme of a villain from the contest you'd need to either change them enough that it wasn't really the same, or get permission from >G and the original submitter.
It's be easiest just to take an idea from it and make something different enough to be yours.