None of the ones you've listed are offensive or off limits. Even atheists naming their kids Abraham or Moses isn't unbearable or rude.
- Omri - not a favourite of mine, but not a problem to use. I like Oren (which is also Hebrew) more just as a name, or Uri.
- Judah - I might guess that a little Judah was Jewish but it's not a problem for him not to be, its just not common. And a non-Jewish Judah is less remarkable, to my ear, than a non-Jewish Yehuda, though most Christians I have met by this name family are just Jude. I happen to really, really like Judah/Yehuda for my own list.
- Asa - I like it, but happen to like Avi, Ari, or Amos more. Just saying aesthetically. Not a problem to use.
- Avi - I like this a lot, along with Avram.