Use at the invitation of.
James went to Paris at the invitation of Eva.
Of course in such a short sentence that sounds rather formal. So I might use
James went to Paris at Eva's invitation.
The other phrases you mention are rarely used.
There are only five uses of 'at an invitation from' in all of Wikipedia.
By contrast, there are 2,756 uses of 'at the invitation of' in Wikipedia.
Using on, as in on an/the invitation from/of, does not sound natural.
This coincides with the results of the phrases displayed on Google Ngrams:
This Joyce Wikipedia article was started in 2001 and the earliest appearance of the sentence you found is from this version, by user Dharmabum420 (probably a native speaker) dating from 15 December 2005, as
Joyce headed to Paris in 1920 at an invitation from Ezra Pound, supposedly for a week, but he ended up living there for the next twenty years.
Some people, even native speakers, use unidiomatic English.