Languages

There are three main languages in the Enclave: in order of importance, they are Common, Dwarvish, and Orcish. All three are spoken and written.
Common is spoken and written fluently by almost everyone except a few reclusive Dwarves. Most Humans and Halflings know Common only.
Dwarvish is spoken and written by almost all dwarves and many members of other races (particularly Gnomes), although few non-dwarves can speak it like a native.
Orcish is most commonly spoken by Half-orcs-orcs (sometimes as a point of pride), but there are some of every race who have taken an interest in it. The grammar is simpler and the vocabulary smaller than Common or Dwarvish. Orcish as written by Enclave residents tends to be very simple and is not in widespread use. People who have encountered orcs outside the Enclave (and lived to tell the tale) report that 'Enclave Orcish' is somewhat different than 'Outside Orcish', but they are mutually intelligible.
The Magical Library has books written in other languages, including Elvish, though few still remember how to read them.
All three of these languages have rich cultural lives in Enclave society, including abundant stories and songs. There are many written works in both Common and Dwarvish on a very wide variety of topics in the Magical Library. The Magical Library has several ancient books in Orcish, but they differ from Orcish as used in the Enclave, so they are difficult to understand. Few books have been written in Orcish by Enclave residents.
Elvish is known from several books in the Magical Library. Nobody knows how it was spoken, but a few sages at the University and the Magical Library can puzzle through some of it.
The Magical Library also has some ancient books and scrolls in other languages. Some of these resemble Common or Dwarvish and are somewhat intelligible. Others use completely different words/pictographs/scripts, and nobody knows what they mean.

Game mechanics

Uses the GURPS 4e rules (p. B24), which means:

Everyone gets spoken and written Common for free

You can spend character points to be broken/accented/native in Dwarvish and Orcish no matter your race (i.e., 6 points for native spoken and written)

Elvish is available, but only broken written (1 character point). Scholars who work intensively with Elvish writings in the The Magical Library or the University might have accented written (2 character points).