As per your request, I have striven to learn what I can about the Orcs’ writing system. I've managed to gain something of a tutor, though his efficacy was limited by cultural restrictions of some sort. He would only agree to teach me some of what I have included below.
The Orcish script, which is visually similar to Skyrim’s Dracoglyphic alphabet, is a runic system comprised of 23 base symbols. The alphabet is ordered as B A D K TH R O L V M F I Y N W Z U S SH T G E P, which seems to have been chosen for the largely symmetrical pattern of opposing glyphs. The pronunciation of each letter is generally the same as its Tamrielic counterpart, though their vowels rarely change sound and Y is only a consonant.
Each symbol is composed of one baseline and two slashlines. The vowels, and SH and TH, are the only symbols with triple intersections. Consonants appear to have been given baselines correlative with their speech patterns; lip-defined consonants (B, P, V, M, with W and N as the exception) are horizontal, whereas tongue-defined consonants (the rest) are vertical. There does not seem to be a strong pattern to the slashlines in consonants, and the alphabet appears to have been designed largely for simplicity of form.
A relatively modern invention of Orcish script is the combination of two runes onto one. This only applies for runes that share the same baseline, and the letter that comes first is to the left (horizontal line) or top (vertical line). Slashlines are allowed to touch across letter boundaries so long as this does not create ambiguity in which glyph is meant to be conveyed.
I have been fortunate enough in my travels to befriend an Orc to the point where he was willing to write out an alphabet primer for me, which I have attached along with a sample of other text I have collected from rubbings.
Although the Orcs lack a distinct H symbol, it is present in their language as a diacritical mark. A
\ added to a symbol indicates that the H comes before the main letter, and a
/ addition indicates a following H. The exceptions, of course, are SH and TH which have their own symbols.
An alphabet primer
The word “Cyrodiil”
(Note: this provides an example of Orsimeris’ phonetic transliteration for words spelled in ways their language does not use. Literally, it reads SI-RO-DI-IL)
The “Holy Name of Gortwog”
(Go-rt-w-og gro Na-go-r-m)
The Skyrim Strongholds
(From top to bottom: M-or Kh-a-zg-ur, Du-sh-n-ikh Y-a-l, Na-rz-ul-b-ur, L-a-rg-a-sh-b-ur)
Lastly, these symbols are used for the "gro-" and "gra-" in names. This is the only mainstream use of a triple glyph combination, and with two distinct baselines as well. The arc of the R serves double duty for the vowel, which is turned orthogonally to the rest, giving a vertical baseline for A and horizontal for O, contrary to the usual practice.
I hope to acquire more samples of Orcish script in the future, though as yet I have only seen these directly. The Orcish merchants and wise women with whom I have met have guarded samples of written Orcish jealously, and I was only able to gather the Stronghold names because they are carved on road signs in Skyrim.
From what I have can tell, Orcs consider names lucky if they can be written fully compressed or require full expansion, and try to avoid symmetric names (Orcish palindromes can use the letter’s pair in the alphabet order as well) for reasons of hubris. It is strange, then, that the Orcs adopted “Orsinium Novum” of the Cyrodiilic for the name of their new city, since Novum is perfectly rotationally symmetric.
Perhaps it is a mixture of chance (alternating baselines are impossible to compress) and pride in their new-built city, which remains frustratingly inaccessible in the most part. Even I have yet to be granted access to the Tradeyards, and my dealings with the city-merchants are always in the foothills with the city nowhere in sight.
I hope this report finds you well, and that some knowledge of their script may prove beneficial in your relations with the Orcs. I would advise against demonstrating any skill in this regard, given their proclivities towards secrecy with respect to their language.