The 3-letter title was used as an identification code when Ushio (the composer) was composing the music and getting feedback in the movie production. 
Although it's a premise of concept-based composition, at first, like my ordinary work, my job was to write a whole song and gave it to them. Since the song would be selected according to the movie scene, I put a 3-letter title as an identification code.
... while it doesn't answer the question at all, that's the very reason why he chose to use it. 
Because it's not based on orders, I wanted them to use it without giving any pretext such as "this is the meaning of the song". With that remnant, I also wanted the listener of the soundtrack to have same thought.
However, Ushio explained that it's not random at all. 
However, it's not a random 3-letter word. "htb", the 12th song on 1st disc, is another version of "heartbeat" from the 1st song on 2nd disc. The hints are more or less there.
The first and the most important song is "inv". 
While Bach's Inventions can be considered as a musical excersise for fingering, at the same time, at that time period, it's also a collection of song to understand the beauty of clavier (i.e. piano) song. After it's understood, it became a base to create such a beautiful clavier song. I thought it's matching with the movie's theme. Therefore, the "Invention" was played along the whole movie. That become the "inv" tracks.
Since "Invention" can be analyzed (separated) into 3-part, I also separated the movie into 3 parts. Each part has its own "Invention". However, "inv" is not a whole "Invention" itself, but it depends on the context of the movie. For example, when somebody said "This scene's "inv" uses only the tone row of "Invention" part 1", I disassembled and rebuilt the song.
(Spoiler ahead: the meaning of the song related to the movie, including the ending)
After Shouya overcame his guilt in primary school, he created a new way of communication. The story is about "communication practice", so I used musical exercises. The song was based on creating a whole new world when practising the communication. When thinking about it, Bach's Inventions (Inventions and Sinfonias) came to my mind.
Regarding the ending, when Shouya and Shouko entered the cultural festival, the last-7 measure of "Invention" was played, and that's the first time the whole figure of "Invention" was known. At that time, Shouya's "practice" was over.
The only other title which was explained was "lit" 
The last song "lit", which was only played 2 times, means "light". This movie, which is about achieving the light, ended with this song attached.
: Interview after the screening (Japanese)
: Interview on official site (Japanese)