The primary language of Sadakoyama is called "Kagaku", which is the same as the word for science. It is similar to Japanese and is spoke throughout the country. It forms the backbone of Sadakhan communication because of the nation's emphasis on science and education. Everyone in Sadakoyama is required to be proficient in it. Kagaku, as a language of science, is very precise; there are no homonyms or multiple meanings of words as in other languages. This makes it awkward to use in daily life and near impossible to use for literature or poetry. Kagaku is a refinement of an older language, "Wen" that forms the common root of most of the Sadakhan languages.
Wen is similar to Mandarin; Where Kagaku is flexible and able to absorb new loan words, Wen is less so. Wen is extremely formal and its use in Sadakoyama is similar to Classical Greek and Latin in 19th Century Europe; To lend an air of solemnity and dignity to the few ceremonies the Sadakhan celebrate and for literature and poetry—most of the works of Sojunism are in Wen. The only place where Wen is used on a regular basis is in the Sojun sanctuaries in the Mount Sadakoyama region.
There are dialects of Wen, the primary one being "Zou" (similar to Cantonese, but less differentiated from Wen as Cantonese is from Mandarin; more akin to the relationship between British and American English). Zou is the primary language of Yushan and Goliad, who will speak Zou in daily life, with Kagaku being used for science and education work, and usually Mercanti as an additional language.
Khandava, Marsei and Beaumonde have their own unique linguistic traditions. Khandavan is based on Syrixian roots, but has so highly diverged from that language as to be mutually unintelligible. (There was once a thriving culture in Khandava originating from ancient Syrixian expats; the civilization collapsed but the people continued to occupy the region and retained their language even after being uplifted by the Sadakhan.
Marsei speaks a French-similar language (Archlancer?) that like Khandavan, is highly diverged from its source, called "Marceline". There was an early, Provence/Tuscan like civilization there before the Sadakhan that was largely wiped out by a volcanic eruption, though enough speakers survived to keep the language alive until the Sadakhan came. The civilization's rich literary legacy helped as well. Marceline, unlike Kagaku, is highly figurative and forms the basis of much of Sadakoyama's cultural life. It is widely spoken in Xanadu as well, and is the second most common language in Academy City.
Beaumonde speaks a unique creole of Marceline, with frequent borrowings of words and phrases from Khandavan and Zou; it is said if you want to get anywhere with a Beaumondi just speak Mercanti.
Mercanti is widely spoken and is the second-most common tongue overall, and can be relied on throughout most of Sadakoyama.
Nearly every language in Eras is spoken by someone in Academy City, sometimes even dead ones.