Ossetia following the events of August 2008 are ethnic Georgians, whilst most of those who fled from Abkhazia after Georgia's defeat in 1993 were ethnic Mingrelians (and local residents who abandoned their homes when Georgian military personnel were finally ejected from Abkhazia's Upper K'odor Valley on 12th August 2008 were mainly ethnic Svans).
Ossetia; the Abkhazians have raised no objections to Mingrelians staying in, or returning to, the south-easternmost province of Gal, where, whatever the (disputed) ethnic origins of these locals, there had been a preponderance of Mingrelian-speakers for decades, and Svans who did not take up arms against Abkhazians during the war or thereafter are free to live in their homesteads in the K'odor Valley.
Within Georgia, because of census-practices since circa 1930, no-one knows how many Mingrelians or Svans there are or, amongst each of those ethnic groups, how widespread is the knowledge of Mingrelian and Svan--there are only negligible numbers of Laz in Georgia.
Back in the days of glasnost' some Mingrelians living in Abkhazia voiced their concerns at the way their language/culture was ignored for the greater good of Georgian, and the backlash that such talk occasioned was not confined to verbal assaults.
With particular reference to Abkhazia, the exiles in whose repatriation the Abkhazians are most interested are the descendants of those Abkhazians who migrated to the Ottoman Empire at the end of the great Caucasian War (1864) or following the Russo-Turkish war of 1877/8, a population-shift which denuded Abkhazia of its native inhabitants and created the opportunity for the start of large-scale inward Mingrelian migration, something which became state-policy under Stalin's anti-Abkhazian campaign from the late 1930s and which had such a disastrous consequence for the republic's ethnic balance, Abkhazians forming only 17.
CRIA: How widely spoken are Mingrelian, Laz and Svan in (and outside) Georgia?
Arnott is good on relationships, too: "Among the Mingrelians
of the Caucasus, arguments between married couples were usually settled by the local chief who solved the problem by selling one of the pair as a slave.