Adûnaic derived from the related Bëorian and Hadorian tongues — collectively called Taliska — of the Atani, and during the Second Age a Bëorian accent still survived in parts of Númenor, most notably in Emerië and around the harbour of Andúnië. Most of the House of Bëor had been killed after the Dagor Bragollach, and therefore the Hadorian accent had become most prevalent.
Adûnaic seems not to have been influenced by the language of the Second House of Men, the Haladin tongue, at all: when the Númenóreans returned to Middle-earth in the Second Age, they did not recognise the peoples of Enedwaith and Minhiriath as their distant kin, because these spoke Haladin languages.
The Westron or Common Speech, widely spoken in Middle-earth during the Third Age, was largely derived from Adûnaic. The Black Númenóreans of Umbar and other Númenórean colonies spoke a related tongue during the Third Age called Black Adûnaic, which was closer to the old tongue as it was not enriched with Elvish influences.