It doesn't need to be spoken by the majority to be the most commonly spoken language, either.
That is, the majority of Igala is 50% of the population plus one...but if everyone speaks a different language except for ten people who speak Common, then the most commonly spoken language is still Common.
Speaking of Common, of the 25 established Igalan nations (Avon, Barius, Baron, Cotiego, Curatori Faiyar, Doma, The Dwarven Holds, Evringshal, The Far North, Forfeit Isle, Gre'par'th, Gwa'aag, Inustan, Kalshana, Nekonia, New Kilian, Riva, Solasia, Tan'yama, Tarania, Theice, Therney, Unostychia, Valth, The Woodlands), Baron, Doma, Kalshana, Nekonia, and Riva are the five nations established with Common being either the national language or the primarily spoken language. In Nekonia the official language is High Nekonian, but few actually speak the language and all official documents are also produced in Common; in Kalshana the official language is Common. In both Nekonia and Kalshana some communities exist where the respective "native" or non-Common language is spoken.
The peoples of Barius, Dwarven Holds, Inustan, Theice, and Valth each speak their respective languages. The usagijin of the Woodlands do so as well, although multilingualism is very common; Common, High Nekonian, High Elvin and Inustani are the most commonly studied languages.
As for the other 14 nations:
The people of Evringshal, the Far North, Tarania, and Therney likely speak Common.
Avons probably speak demonic. Tan'yama might speak High Elvin, Common or both. Solasia would have a mixture of languages, at the least Draconic, Griffonic, and Dwarvish, if not also Common. New Kilian might have a mutation of Nekonian or a Nekonian-influenced dialect of Common, being a country whose people originated from nekojin migrants in pre-Nekonian days. Cotiego might speak Common and/or demonic and/or a mutation of Inustani, as its werewolves came from pre-Inustan lands.
There's no information on Unostychia. I'm guessing that the people of Curatori Faiyar, Gre'par'th, and Gwa'aag speak Common.
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edit: as for how it spread?
Baronians established Doma. Domans established Riva. The three nations have maintained ties over time. Domans and Nekonians have traded for eons of your years, as well Nekonians have been migratory in their distant past. Kalshana borders Nekonia. Baron maintains diplomatic and economic importance in Igala's west, Doma, Nekonia, and Kalshana do so in Igala's east.
Igala doesn't really have all that much wilderness. That which is inhabitable is, by and large, inhabited. That which would not be inhabitable is inhabited, thanks to A Wizard Did It (21st century England didn't have that!). The largest space of theoretically uninhabited land is between Baron, Avon, and Gwa'aag in the southwest.