To answer your last question first: Use a dictionary that follows a widely-accepted standard; that's what IPA is for. If you really want to use Merriam-Webster's pronunciation guidance, you'll need to refer to their own notes.

Going back to the source of your table: I wouldn't trust it. There's a lot wrong with that page, which appears to be just a personal opinion. In particular the author has ignored the distinction between \ə\ and \ər\ in the M-W guide.

I think the examples are the author's own, and I don't think the author is a native speaker of a common dialect of English. Some examples only make sense in a rhotic accent (seemingly treated as default by Merriam-Webster), while others don't make sense in the same accent.

Some examples:

• Oxford has /wəːk/, not the /wɝk/ implied.

• M-W has \ˈwərk. We can't neglect the r in that transcription as the author of the page you linked does (see p.2 of the pronunciation notes I linked in my first paragraph).

• As I commented, courage doesn't belong in the first list, in (most) English or many American accents:

  • Oxford: /ˈkʌrɪdʒ/ would put it in the second list (ʌ).
  • M-W gives two pronunciations: \ˈkər-ij , ˈkə-rij\ of which the first does fit the ɝ list. But the second fits the ʌ list. The notes under \ˈər-, ˈə-r\ in the pdf I linked make this clearer.
  • As such a poor example for either list, including it at all is misleading.