Prior to the fall of the gods there was no universal or common language, not ever a true lingua franca, since the rise of Dragon rule and the Imperium the language known as Low Draconic has spread widely, as it is used for all official matters within the Imperium. (High Draconic can only be properly spoken by dragons and other such creatures.) An educated person should know at least the basics of Low Draconic and it has come to form the basis of what is known as the Imperial Tongue, a mixture of simplified Low Draconic with loan words from, well, just about everywhere.
The dwarven language is widespread, even beyond the dwarves, who have different dialects (occasionally radically different from each other) for each clanhold though the written language is nearly the same whatever. So one can be said to be fluent in spoken Ruby Dwarven and should be able to make themselves understood to a Emerald Dwarf but with much greater difficulty to the distant Jadite Dwarves but using writing they should be understood by either.
The elven language is musical and complex, the tendency toward cultural conservatism and the fact that the long lived elves often travel to visit their more distant cousins have combined to keep linguistic drift to a minimum even between widely dispersed elfin communities. That is not to say that there are not the occasional miscommunication especially with the elven groups that are more enmeshed with the quickly changing human cultures.
The giants had their own languages, with dialects for the various giantish cultures, but it is barely kept alive in a primitive state by the small number of surviving giants on the fringes of the Sea of Stars. A few scholar still study it as well trying to puzzle out the secrets of the lost giantish civilization but they know it almost exclusively as a written language.
Many nations, such as the Eosiante, maintain their own language, though words leak in from the Imperial Tongue (and words migrate from it to the Imperial Tongue as well). Scholars of rare and lost languages are always in demand among those seeking forgotten treasures and knowledge: tombs and temples, wizard’s towers and libraries, are all sought.for power and plunder.
Languages, speaking, reading, understanding them, is a valuable talent in the Sea of Stars. So, do not neglect your studies.
Notes: Image “Antipodes — English” by wanderingYew2 (thanks for 3M+ views!) is licensed under CC by 2.0.