外海 has two readings がいかい and そとうみ. What is the difference of the two? Personally, I am under the impression that がいかい is the common reading because of its similarity to the word 外国【がいこく】. However, I have encountered situations (some songs) where そとうみ has been used instead.
The NHK Accent dictionary and the 大辞林 include both がいかい and そとうみ readings as valid for this term.
The デジタル大辞泉 lists the first definition of kaigai and sotoumi as synonyms for a sea that is not bound by the continent, or to the open sea that is not close to the continent. However, the second definition of kaigai, which is more metaphorical, means foreign lands, and I couldn´t find this connotation in the definitions of sotoumi. Here are the definitions for がいかい and そとうみ.
Additionally, there is the Buddhist term げかい that uses the same kanji.
Also, there is at least one person name with these kanji (とのがい).