One of the Bell Labs history "A History of Engineering & Science in the Bell System" series covered overseas radio transmission in detail. Most larger libraries have these and it's worth checking out. I'm not sure which volume of the series covers overseas calls.
They used a combination of long wave and short wave transmissions, using whichever happened to afford the best signal when the call was made. I sensed that engineers had to babysit every call adjusting the signals as necessary. They had to manually consider a variety of electronic and atmospheric conditions. The ability of equipment to "lock on" was limited in the early days.
I believe later on they did use an elementary form of encryption to protect privacy. Not enough to guard against a determined listener but enough so that a casual listener couldn't understand.
While radio transmission technology grew sharply during WW II I don't think much was applied to overseas radio calls. Instead the emphasis was on designing, building, and laying the overseas Atlantic cable. Made a world of difference when that went into service.
I don't know much about overseas Pacific telephone lines, where the distances are so much greater. There was a British company, "Cable & Wireless" that had telegraph service. The company maintained relay stations on little islands with some people and equipment. Very expensive. I'm curious as to when Hawaii got radio-telephone service to the mainland US and then cable service.