"When Asa heard the words that Oded the prophet spoke" or "When Asa heard the prophecy of Oded the prophet." The phrase "the prophecy of Oded the prophet" defines "these words."
Many versions, including the UDB, make this passage read, "the prophecy of Azariah, the son of Oded the prophet." They do this in order to make the sense agree with [2 Chronicles 15:1](../15/01.md). Translators will probably want to do the same in their versions.
The words "the disgusting things" refers to idols. Having his people remove or destroy the idols is spoken of as if it were driving them away. Alternate translation: "got rid of the disgusting idols" (See: [[rc://en/ta/man/translate/figs-explicit]] and [[rc://en/ta/man/translate/figs-metaphor]])