1. He just(adv) arrived after breakfast.
  2. He arrived right(adv) after breakfast.
    Are these two sentences OK?
  3. He arrived just(adv) after breakfast.
  4. He right(adv) arrived after breakfast.
    Are these two sentences OK?

1, 2, and 3 are correct but have different meanings. 4 is incorrect.[YSaerTTEW443543]

TOEIC listening, photographs: Archaeological site[YSaerTTEW443543]

What is the nuance of grammar for using the adverbs - just and right?

I’m not sure what you mean by asking about the ‘nuance of grammar for using the adverbs’, but these are the differences in their use above:

He just arrived after breakfast - probably indicates he suddenly and unexpectedly turned up after breakfast. ‘Right’ cannot be used in this sense.
(Here ‘just’ can be defined as ‘simply’ - He simply arrived… He was not expected, but he simply turned up.)

He arrived just/right after breakfast - he arrived very soon after breakfast was finished. ‘Right’ and ‘just’ are interchangeable.