The most important concepts to keep in mind for this post are Synthetic Languages, agglutinative and fusional inflection, nominative-accusative alignment, prefix/affix/suffix.
Links: http://i.ironau.ru/ocherk/OssetianGrammar.pdf here is the paper I used for reference and examples. The paper is a compilation including two versions of V.I. Abaev's published works, and I find it to be incredibly useful. And as always, the phrasebook transcription provided at http://ossetians.com/eng/news.php?newsid=443&f=35 for supplemental reference.
Inflection of agglutinative and fusional elements: Nouns
Before continuing on, I would like to reiterate the difference between agglutination and fusion, agglutination uses multiple separate morphemes with each morpheme representing a separate piece of information, while fusion uses affixes that can contain multiple meanings, such as plurality, grammatical gender (in languages that use this), and case inflection, all in the same affix.
Perhaps one of the easier examples to demonstrate, of Ossetian's use of agglutination, is the plural marker '-T-', which is the standard marker in most cases. This singular letter, while representing the grammatical feature of plurality, does not give context beyond that, and requires additional morphemes to convey extra information.
Ossetian's fusional aspect is found in usage such as the suffix '-æм'. The allative case ending '-æм' for nouns is also the 1st person plural ending for verbs, such as кæнæм 'we are doing...'
Taking an example from the above link, I will explore the system of inflection as it appears in the different cases for nouns:
The example word is 'сæр' (head).
Nominative: - сæр - сæртæ
Genitive: - сæры - сæрты
Dative: - сæрæн - сæртæн
Allative: - сæрмæ - сæртæм
Ablative: - сæрæй - сæртæй
Inessive: - сæры* - сæрты*
Adessive: - сæрыл - сæртыл
Equative: - сæрау - сæртау
Comitative: - сæримæ - сæртимæ
* The case-inflection for the Genitive and Inessive cases is listed as being the same, all you need to remember for this is that similar to English, context will tell you which meaning is intended.
I mentioned that the '-T-' plurality marker is the standard marker in most cases, some of the situations where other markers are used include:
Within what Abaev categorizes as 'kinship terms', some specific words inflect differently than normal, by adding an 'æлтæ' plural-marker, with examples attested as 'мад' ('mother', singular) and 'мадæлтæ'' ('mothers', plural), 'фыд' ('father', singular) and 'фыдæлтæ' ('fathers', plural), and lastly, 'æрвад' (relative, singular) and 'æрвадæлтæ' (relatives, singular).
Listed in Abaev's work is several examples where specific nouns don't inflect in a manner that you would expect them if they followed the general pattern:
Ус 'woman' is marked in the plural as 'Устытæ'; basically, the plural is marked as if the stem word was 'Уст', but because it is not, in theory, the plural should technically be marked as 'Устæ'.
Хъуг 'cow', theoretically, should be marked in the plural as 'Хъугтæ', but in reality the plural in this case is marked as 'Хъуццытæ'.
фыр 'ram', is marked in the plural as 'фырытæ', despite the fact that the regular pattern would theoretically mark it in the plural as 'фыртæ'.
куыдз 'dog' is marked in the plural as 'куйтæ' (куыйтæ) instead of 'куыдзтæ'.