The Akaali languages were any of the dozens of languages spoken by the Akaali on the Akaali homeworld.
In 2151, Enterprise NX-01 explored the pre-warp civilization. The acoustic relay picked up "dozens of languages" from the planet, Communications officer Hoshi Sato joked that she could spend ten years studying the planet. She noted that their name for their own species was "Akaali", but setting up a translation matrix for which language they would need depended on the landing site they selected. (ENT: "Civilization")
From examples of written language seen in the episode, it would appear that it could be written both horizontally and vertically.
According to a note in the set requirements section of the call sheet, an "open leather bound book with alien writing and drawings of microbes
" was used in the apothecary
Examples of spoken language
While investigating the mysterious deliveries, Riaan and Jonathan Archer were discussing his curious habit of talking to his dog Porthos when the universal translator malfunctioned.
Riann: My mother bought me a tusorop ko once, but it tuproya plo dak.
In the pronunciation guide from the script of "Civilization", the two Akaali statements in this sentence were phonetically notated as "too-so-ROPE ko" and "too-PROY-uh plo DAHK".
Archer: What was that?
Riann: Deshi teeg ti'lat mokel. Proyal nil'shan teeg? Ti'lat? Proyal nil'shan teeg–
The script pronunciation guide for "Civilization" made it clear this statement was to be pronounced "DAY-she teeg tee-laht MO-kel. proyl nil-shahn TEEG? tee-LAHT? proyl nil-shahn TEEG?"
(Archer kisses her, to correct the universal translator on his communicator behind her back.)
Riann: Tishik a'plal?
In "Civilization"'s script pronunciation guide, this question was notated "tee-SHEEK ah-PLAHL?"
(Archer tries to correct it again.)
Although the "Civilization" script notated how these Akaali statements were to be pronounced, their meaning in English wasn't scripted.