Throughout the various parts of the UAC Facility, particularly Olivia Pierce's office and the underground church, as the invasion occured the demons wrote phrases and runes in their language using the blood of the slaughtered UAC workers. The writings are also located in Hell, although they are engraved into rocks in a bright red material instead of blood.
From the concept art, although it is slightly difficult to decipher, there are around 25 unique language symbols, meaning a full alphabet can be created.
The symbols are re-used constantly, and if an alphabet that translates to english letter is created it would not make that much sense, but from the simplicity and repetition of the symbols, the words are simple. A possible explanation for the writings not making sense could be that the demonic language, like regular languages have evolved over time, or the chaotic nature of Hell means demonkind does not need a properly structured language system.
These refer to 12 unique symbols scattered throughout the UAC Facility and Hell.
Unlike the alphabetical writings, these runes are unique, and are used for ritual purposes, and share the same symbols as the powerup Runes available in the campaign.
In the UAC containment cages, the rocks are enscribed with various runes and writings, most notably the pentagram rune and the hexagon with 5 rune chains connected by alphabetical writings.
The runes seemed to be a binding agent, as until the invasion occured brutish demons like the Hell Knight were held in the containment box. Not much is known about their purpose otherwise. In Kadingir Sanctum, in the area where the Doom Slayer was imprisoned, one can see the bright material runes etched into the walls, and even the tomb had a plethora of these runes and alphabetical warning to bind and warn demons that would see the tomb. One can presume the runes with the bright material are significantly stronger and act as physical binding agents to whatever is trying to be contained.
The runes can be found on windows or floors of the UAC facilities, particularly areas with hanging gore and viscera. These are written in blood, although unique variants exist where the runes are written in the floor beneath a puddle of blood with the same bright material like the ones inscribed in the tablets of Hell.
In Hell, the runes are inscribed into various objects, Gates, doors, the Skull Keys etc. various rocks, like the ones in the Hell arena where you fight the Cyberdemon have yellow runes engraved into them, or the doors of the Argent D'Nurian arenas, where the doors have runes enscribed into the center lock which change colour based on the amount of demons killed;(Red Locked, Yellow Halway, Green Open)
Tablets retrieved from Hell also have these writings, ranging from cuttings in stone, to the bright writings on important tablets which can be analyzed.