From Frommer's Language Log guest post we know that there are six noun cases, and that most of them have several forms. This is the list of known forms the cases can take, based on the existing text Corpus.
|Subjective||(no suffix)||subject of intransitive verb|
|Agentive||-l, -ìl||oel, tìngayìl||subject of transitive verb (called ergative in linguistics)|
|Patientive||-t, -it, -ti||katot, txe'lanit, kifkeyit, ngati||direct object of transitive verb (called accusative in linguistics)|
|Genitive||-ä, -yä||txonä, oeyä||may cause modifications of the noun stem|
|Dative||-r(u), -ur||ngaru, frapor, eylanur||indirect object|
|Topic||-ri, -ìri||oeri, fìskxawngìri|
Unlike several of the verb infixes, for which Frommer has identified some forms and meanings, the noun case markers have been determined almost entirely by analysis of the existing corpus with some help from the word list from the ASG and our knowledge from the Language Log post (LL) about what the cases are.
We do know that the case markers may have several forms. We do not know the rules for determining which sorts of words get which case marker variants, though anyone with some college-level linguistics study in phonology and morphology should be able to make some intelligent guesses. Hopefully a full grammar will be published sooner rather than later.
Note that the names Frommer has chosen for the cases are not in accord with current linguistic terminology. What he calls the "agentive" is usually called "ergative," and what he calls "patientive" is usually "accusative."
As of 2009 December 30, we have three attested forms for this case, -l, as in oe-l nga-ti kam‹ei›e I see you (UGO), awpot set ftxey aynga-l now (you) choose one (ASG, Hunt Song), Neytiri-l yerikit tolaron Neytiri hunted a hexapede (MSNBC), and -ìl found in oe-ri tìngay-ìl txe'lan-it t‹iv›akuk let the truth strike my heart (ASG, Hunt Song).
As of 2010 January 20th, we have three attested forms for this case. The first discovered is -ti, which came out in UGO, the very important greeting, oe-l nga-ti kam‹ei›e. Other sightings of this allomorph are Kelutral-ti skiva'a to destroy Hometree (BtS), horen-ti-sì lì'fyayä leNa'vi and the rules of the Na'vi language (AMFP).
As of 2009 December 26, there are two attested forms of this case.
The -ä form appears to occur after consonants, as well as the syllabic resonant rr, and after diphthongs ending in y: trr-ä sì txon-ä of day and night, ayzìsìt-ä kato rhythm of the years (ASG, Weaving Song), tìftia kifkey-ä study of the physical world (SciMag).
As of 2010 January 20, we have three forms attested for the dative. The first, -ru is attested on pronouns and other words ending in vowels. oe-ru (numerous locations), ... nga Na'vi-ru yomtìyìng you will feed the people (ASG, Hunt Song).
The -ur form appears to be the form for words ending in a consonant, as in ayeylan-ur oeyä to all my friends (AMFP).
There is also a -r allomorph, found in lu oe-ru aylì'u frapo-r I have something to say (BtS), fpole' ayngal oe-r you sent to me, zamolunge awngar (they) brought to us (AMFP). The choice between the full -ru and shorter -r ending is a matter of personal taste, "Ngar and ngaru are used interchangeably--pick the one you think sounds better in its position" (RaN).
As of 2010 January 20, we have two attested forms of the topic marker. We have -ri, in oe-ri ta peyä fahew akewong ontu teya längu my nose is full of his alien smell (LL), ayngari zene hivum you have to leave (BtS).
The other form is -ìri, again with a single attestation, fìskxawngìri tsap'alute sengi oe I apologize for this moron (TO).