Excepting Valarin, Khuzdul was the first language to be created in Arda. It was invented by the Vala Aulë who taught it to the Seven Fathers of the Dwarves. However, due to the fact that Ilúvatar jealously kept the honour of 'Firstborn' for his own creation, the Elves, the Dwarves were put to sleep, so Khuzdul was not the oldest language spoken in Middle-Earth.
We have all of two samples of Khuzdul in our whole corpus. The sentence "Baruk Khazad! Khazad ai-mênu!" (Axes of the Dwarves! The Dwarves are upon you!) and "Balin Fundinul uzbad Khazaddûmu" (Balin son of Fundin, Lord of Moria). Khuzdul is believed to have a system of triconsonantal word bases. For example, all noun forms, adjectives and verbs relating to the subject for dwarves come from the roots Kh-Z-D (Cf. Khazâd, Khuzdul, Khazâd-dum). It also seems to have a 'construct state' like Hebrew, in which a word placed before another forms a genitive. Khuzdul also frequently omits the copula (see Russian). These are all the known or inferred (read 'guessed') forms of a Khuzdul noun:
-1u23u Construct State Singular *
-1a2u3 Construct State Plural
-1a2a3 Adjectival Pattern
-1i2i3 Adjectival Pattern
-1u23ul Adjectival Pattern *
-ma1a23 Past participle *
Forms asterisked are those forms that are highly experimental.
Tolkien claimed that "this tongue has been sketched in some detail of structure, if with a very small vocabulary" (Peoples of Middle-Earth: 300) We await more information to be published.
For more information on Khuzdul (which has been 'fleshed-out' or 'completed' by some enthusiasts, but not with much success) visit Helge Fauskanger's Khuzdul article at http://www.uib.no/People/hnohf/khuzdul.htm.