How was the first overseas phone call possible back in 1927?
The system you're referring to was described briefly in the Bell System Technical Journal in 1935. Most of the article is about measuring the advantages of the (then brand-new) "single-sideband suppressed carrier" (SSB) modulation over the conventional double-sideband amplitude modulation (AM), but it mentions some of the history of transatlantic telephone in passing, and says that it used shortwave frequencies of 5 to 20 MHz (5,000 to 20,000 kc in the notation of the time).
Waves at these frequencies are capable of being refracted by the F-layer of the ionosphere (a layer of charged particles 200 - 400 km above the Earth's surface, which was theorized in the 19th century, but first seriously measured between 1925 and 1927). Refraction of signals by the ionosphere makes it possible to communicate between points on the Earth's surface up to 3,000 - 4,000 km apart in a single "hop". This is just about enough to cover the distance between Newfoundland and England, but it's also possible for a signal to take multiple "hops" — conveniently, seawater makes a good reflector of radio signals.
The relatively wide range of frequencies (a 4:1 ratio) was used because ionospheric conditions vary with time of day, time of year, and the solar cycle — generally, lower frequencies perform better at night, in winter, and during solar minimum, while higher frequencies perform better at midday, in summer, and during solar maximum.
Bouncing the radiowaves like Marconi did when "they said it couldn't be done" is one of the options for over-the-horizon radio communication, but the Wikipedia article on Rugby Radio Station mentioned in the comments says:
In 1927, a second transmitter was installed to initiate the first transatlantic commercial telephone service; linking New York and London on 60 kHz using single-sideband modulation.
At this frequency it is most likely the effect they used is groundwave propagation: at such (lower) frequencies, waves can travel as "ground waves", which can and do follow the Earth's curvature. This works particularly well over conductive surfaces like sea water.
The 1935 paper "A Single Side-Band Short-Wave System for Transatlantic Telephony" , by Polkinghorn and Schlaack is interesting. Stone knives and bear skins indeed.
Here's an excerpt from an earlier paper "The Propagation of Short Radio Waves over the North Atlantic" Published in: Proceedings of the Institute of Radio Engineers ( Volume: 19 , Issue: 9 , Sept. 1931 ). Of course, mc (megacycles) refers to MHz in the below.
Summary-Transmission conditions for each season are shown by "surfaces" giving the received field strength as a function of time of day and frequency. These show that frequencies near 18 mc are best for daytime transmission. In summer the best frequencies for nighttime transmission are those near 9 mc. In winter an additional frequency near 6 mc is required during the middle of the night. A frequency (such as 14 mc) intermediate between the day and night frequency is useful during the transition period between total daylight and total darkness over the path. Day-today variations change the periods of usefulness of these frequencies. In particular the period of usefulness on 14 mc sometimes extends so that it is the best daytime frequency. Transmission conditions on undisturbed days were found to be the same for the same time of year on different years. These undisturbed transmission conditions are presented by "normal" surfaces. Comparison of these surfaces shows that the higher frequencies are less attenuated in winter. Reception on the highest frequency, 27 mc was best in winter; in summer this frequency was never heard. The effect of solar disturbances on short-wave transmission is to reduce reception on all frequencies. Sometimes the higher frequencies are the more adversely affected. Some of the, possible causes of these disturbances are discussed. From the measurements made on "static" at New Southgate, data on the variation of its field strength as a function of frequency, time of day, and season are given.