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I'm going over the Tirelat grammar to take a break from the vocabulary 
work, and improve the documentation. The current topic is noun cases. 
It's questionable whether I should call them cases at all, since they're 
marked not on the noun but a particle attached to the start of the noun 
phrase. Case and number are fused into a single word. E.g.

saj    zarvi ċik
NOM.PL bare  rock
(the) bare rocks

The adjective and the noun remain uninflected. There may be an argument 
for considering nominative and accusative as the only two "real" cases, 
since there is agreement on the verb for each of those, and pronouns 
have separate nominative vs. accusative forms, but I'll continue using 
"case" for the rest of these noun phrase particles.

As I've mentioned, nominative and accusative are two prominent cases. 
Most intransitive verbs have a nominative subject, and most transitive 
verbs have a subject in the nominative and an object in the accusative. 
The nominative case tends to be used for agents and experiencers, and 
the accusative case for patients (but also destinations and some other 
usages).

The nominative case has three forms: su (animate singular), sy 
(inanimate singular) and saj (plural). This is the only case so far that 
distinguishes between animate and inanimate nouns, although it's 
possible that other cases may make this distinction. The accusative case 
marker is my (singular) or maj (plural).

Some verbs also have an indirect object, which will be in the dative 
case (na/naj, used typically for a recipient or a beneficiary). The 
locative case (vë/vaj) represents the location of an action.

Now for the more interesting ones. Some verbs, of which "veste" (to 
dance) is typical, have an extra subject (kë/kaj). I call this the 
"comitative" case, since the English translations of these verbs tend to 
use "with" where Tirelat uses this case.

Another lesser used case (dy/daj) is one that I haven't had a name for, 
but I'm thinking of "ablative". Typically, it's used for non-volitional 
agents, or the agent of a passive verb, which according to Wikipedia are 
possible uses of the ablative case in Latin, and I've also considered 
using this case to represent the "source" of an action (one translation 
of English "from" or "out of").

Then there are the two remaining cases, which unlike the preceding 
cases, are not associated with particular "argument slots" of verbs. The 
vocative case, used to direct a comment to a particular listener (or 
listeners) has only a single form (ee), not distinguished by singular or 
plural.

The last case (u/aj) is one that I've been calling "oblique", as it 
typically is not associated with a verb; its most typical use is as the 
object of a locative noun phrase.

vë     lak  u      łivi žeġ
LOC.SG over OBL.SG lazy dog
over the lazy dog

However, the "Swallow Song" translation on the Tirelat web page 
(original at http://archives.conlang.info/shi/jhoezan/bibiaghein.html) 
has a couple of unusual usages of this case.

jë-kóta -z   u   zhemi     nallu, u  zhemi     rága
3s-carry-IPF OBL beautiful hour   OBL beautiful year
bringing hours of beauty, years of beauty

ty  rílh -ë-njem  sha mifsi -njem  zhlara-ru -ka -j  u   tegla
and wheat- -bread nor legume-bread refuse-PAS-NEG-GA OBL swallow
And the swallow does not disdain wheat-bread or pulse-porridge, either.

zhúvi, zhúvi u   shúru më-bala-ta -j  na  tegla
open   open  OBL door  3s-set -DEO-GA DAT swallow
Open, open the door for the swallow

I don't know if I should try to account for these cases. Maybe it would 
be better to make a new translation from the original Czirehlat version 
from 2001 (http://archives.conlang.info/kau/sueljei/jhorqaenghein.html), 
or directly from the original Greek.

kóta -z          me  jémi      nállu, me  jémi      rága
carry-IMPF(PART) OBJ beautiful hour   OBJ beautiful year

te  me  ríhl -e-niém  sza mífsi -niém  se   tégla   jelára-kai
and OBJ wheat- -bread nor legume-bread SUBJ swallow refuse-NEG

júvi, júvi se  szúru bála-tai  na  tégla
open  open OBJ door  set -DEON DAT swallow

(Either the "se" or the "OBJ" in the last line must be a mistake, but 
I'm not sure whether "se" or "me" is correct in this case.)