The Distortion World is 1190. I'm going through another Sinnoh playthrough as we speak in order to figure out what Giratina's theme is. But I can offer some specifications about this list in case some of the formatting ends up confusing someone:
- Eterna is, oddly enough, not Eterna Forest. I have no clue what "Eterna" is, but I found that "Secret Melody" is used for Eterna Forest. (ID = 1063)
- "Route" is the theme for Route 209. Day ID = 1025, Night ID = 1054)
- "Cave 1" (ID = 1074) is the theme used for the likes of Oreburgh Gate and other miscellaneous cave themes around Sinnoh, whereas "Cave 2" (ID = 1075) is for Oreburgh Mine and Iron Island.
- "Team Galactic 1" (ID = 1067) is used for the Veilstone HQ, whereas "Team Galactic 2" (ID = 1068) is for just about everywhere else those loveable spacemen invade.
- I'm 99% sure that the "Special" versions of Eterna City and Route 205 are the versions that go unused in the game.
I hope this was helpful!