There are several languages commonly (or less-commonly) used in western Noefra as of 210 AC. Some are tied to race--of these only one is genetically tied to race: Ngyon Toi, the goblin language. All the rest are heritage languages. Included in this list are a few archaic languages and some external languages that characters might encounter.
Almost every humanoid (and many non-humanoids) speak Common as either a first or a second language. It is the descendant of Old Imperial, the lingua franca of the Western Empire. In the 800 years since the Fall of Empire, it has broadened and changed. Still, it's mostly mutually intelligible across the half-continent. Humans and halflings, as well as the demi-races (half-elves, half-orcs, dragonborn, tieflings, aasimar and genasi) usually speak it as a first language. Elves, dwarves, orcs, serpent-kin, and goblins speak it as a second language. The real-world equivalent is English. The script used is called Reformed Imperial, and is a direct modification (and simplification) of Old Imperial characters.
The "standard" dialect, this is spoken in Kaelthia, Rauviz, and Yuuras Zaali. Equivalent to the Received Pronunciation of English.
Spoken in Rabbiton and Baile Craan, this dialect is influenced by Metsae and is noted to be a sing-songy and fluid.
Spoken throughout the Stone Throne, this dialect is heavy on sibilants and nasal sounds.
Spoken in the Dynasty, this dialect tends to chop the ends of words off.
Spoken in Byssia, this dialect of common employs many unique words and fewer specific nouns. Things are described, often poetically.
Metsae (Wood Elf)
The racial wood-elf language, a form of this is spoken by most tribally-oriented wood elves. It is a slowly-changing language, so it is often used for first attempts at communication with widely-separated tribes because it's unlikely to have changed since they last met. Metsae is written in a compressed version of the flowing elven script, but without the geometric patterning of Yonwach. The real-life base language is Finnish.
Yonwach (High Elf)
The ancestral language of high elves, this language is carefully preserved. New words are added occasionally, but the grammar and structure has been unchanged for millennia. Its written form is elven characters. For all but the most disposable writings, the characters and words are arranged into geometric constructs (nested spiraling polygons, arcs, interlocked rings, etc)--different paths through the text reveal different meanings and subtexts. Translating it is notoriously difficult. The real-life base language is Welsh.
A guttural tongue, Ard-teang is the cultural language of the northern orcish tribes. Although they tolerate outsiders learning the vernacular form, the sacred dialects are off limits to those not accepted by the tribes. When written, Ard-teang is vertically-oriented and uses heavily modified elven characters interspersed with runic elements. The real-life base language is Irish Gaelic.
Spoken by dwarves and (historically) by the extinct gnomish race, Bidni-Khel is a language unlike most others. Its closest relative is Too-til, the giant language. Written in dwarven script, which is a debased runic script, Bidni-Khel is written in 4x4 square blocks of characters and can be read in multiple directions. Lying in written bidni-khel is a mortal insult to any traditional dwarf. The real-life base language is Mongolian.
Ngyon Toi (Goblin)
Ngyon Toi is unique in that it's dominantly genetically transmitted. Goblins are born knowing how to speak it. Since a large fraction of communication between goblins is semi-telepathic through their shared memory, spoken ngyon toi is clipped and staccato, with much left unsaid. When spoken by outsiders (who don't share this racial connection), ngyon toi requires significant verbosity and circumlocutions. Objects are described. There is no written form, although transliterations have been made into several scripts and educated goblins can usually write in common. The real-life base language is Vietnamese.
Two such languages are detailed here, although many others exist. These are languages that are either dead (no native speakers) or almost so and are mainly found in written form on monuments and ruins.
Old Imperial (Dead)
The base language of western humanity, the national language of the Western Empire, this is the main academic written language of the Federated Nations. Found all over pre-cataclysm facilities and artifacts, any serious scholar would know how to read Old Imperial. The base language is Latin.
Almost dead, this language is only spoken by the tribes of serpent-kin that escaped captivity in the Stone Throne. The older dialects are found across Fanged Kingdom buildings, ruins, and artifacts. Written in an archaic form of elven script, the base language is Khmer (Cambodian).
These languages are sometimes encountered by adventurers, but they're not the native tongues of anyone living in the Federated Nations.
The language of dragons and sorcery, this language is learned (at the elementary level) by dragon-born as part of becoming adults. Real dragons say that dragonborn speak "kiddie" draconic. Extremely complicated in grammar and syntax, some of the words involved are hundreds of syllables long and any mispronunciation alters the meaning tremendously. Dragon names tend to accrete throughout their lives, reaching thousands of syllables for the most ancient ones. The base language for draconic is Old Church Slavonic. Draconic is not written natively, but transliterations into elven or dwarven script exist.
This language of power was used by the Titans in the First Age. Only fragments still remain, and only in written form. Any spoken versions are extrapolations, guesses at best. It is similar in form (but significantly more complicated) than Bidni-khel or Too-til, its descendant languages. There is no base language for runic.
A relative of Bidni-khel and a fellow descendant of Runic, Too-til is spoken by many giants (especially the educated stone, fire, cloud, and storm giants of the east/south-east). Written in ideographs composed of multiple runic elements, the base language is Kyrgyz.
There are two forms of this language--one spoken by those on divine missions (Celestial) and one spoken by summoned astral beings (Infernal). The primary difference is that Celestial is infused with magic so that anyone can understand it and lying is impossible. Circumlocutions are possible, however. Infernal is a slang form of the same base language and is the dominant working language of the astral plane. Demons also tend to speak infernal (as well as whatever language they learned as mortals, if that was where they started). There is no real-life base language for these.
This family of languages is spoken by creatures native to the elemental planes. Like the Sinitic languages they're based on, these languages are largely mutually comprehensible when spoken by natives. Mortals tend to speak in a mishmash of languages depending on exactly how they learned it.