Hmmm. This is tough. It's very possible that records of your relative exist in both South Korea and the U.S., which is all to the good, but tracking them down is another thing. (It's also possible that records of your relative exist in North Korea, but for the moment I think it's safe to assume that they remain out of reach.) If it were me, I'd look for people who have done similar projects (or at least attempted to track down information on the same period) and then abuse the hell out of their footnotes, or track down other people who were confirmed to have worked/interpreted for Hodge and the U.S. military occupation and see what additional information may be available.

I'd start with this:

• South Korea's national archives might be your best bet, but I'm not sure that the records you're looking for are going to be online. Are you in South Korea? If you speak/read Korean, you'll have access to quite a few more resources.
• U.S. Army Center of Military History publication on the Korean occupation -- Policy and Direction: The First Year by James F. Schnabel. The second chapter in particular looks like a good bet for both sources and information on Hodge's administration.
• South Korea's Ministry of Unification may also contain something if your relative was captured by the North Koreans; they've made efforts to account for the families that were broken by the shifting borders and disappearances before, during, and after the war. But again, I'm not sure these records will be online.
• There's a chapter in the book Languages and the Military: Alliances, Occupation and Peace Building on Korean War-era interpreters. However, I haven't read the book personally and can't speak to the contents apart from a quick look through Google books. The sources there might be useful.
• There's a self-published book, My Father's War, by Hwang Ha-yong (edited and finished by his son, Hwang Sung) on his experiences with the Korean Liasion Office before and during the war. Again, the sources here may be useful, but as Hwang (the son) remarked in the bibliography, many of the records related to the KLO and Special Forces operations during the Korean War are still classified.
• There's a section in Sunny Che's Forever Alien: A Korean Memoir, 1930-1951 that contains an illuminating reference to Korean interpreters who worked for the U.S. government:

The American military was forced to govern the country with the help of Korean interpreters, earning the label of "interpreters' government." Major General John R. Hodge was a soldier who commanded the taking of Okinawa in April 1945, and lacked savvy diplomacy and political training. But as the head of the occupation government, he kept the South from sliding into anarchy and maintained a semblance of order in the post-war chaos.

It is often overlooked by historians that the Korean interpreters, during this critical time, played a significant part in keeping the American government interested in the fate of Korea. These interpreters were by and large educated by American missionaries before the Pacific war and were true believers in the democratic principles of government. By acting as interpreters, they were in a position to influence American thinking and policies toward Korea.

This is an accurate portrayal of how unprepared the U.S. really was for the Korean occupation, by the way. The missionary angle may be extremely useful; Kim il-Sung himself played organ in a Protestant church when he was a kid, and some historians have wondered about the extent to which Christian worship may have influenced the development of his personality cult. Anyway, that's also something I'd pursue (again -- sources!) because opportunities for learning English in Korean society before WWII would have been very limited outside the church.

I hope that helps at least a little. This sounds like a fascinating project!