Albert Barnes Commentary 1 Kings 18:10

"As Jehovah thy God liveth, there is no nation or kingdom, whither my lord hath not sent to seek thee: and when they said, He is not here, he took an oath of the kingdom and nation, that they found thee not." — 1 Kings 18:10 (ASV)

There is no nation ... - This is expressed in the style of Eastern hyperbole. What Obadiah means is this: among the nations and kingdoms over which Ahab had influence, there was no place where the king had not sent someone.

For example, he could scarcely have exacted an oath from powerful countries like Egypt or Syria of Damascus. However, Ahab may have been powerful enough to expect an oath from the neighboring Hittite, Moabite, and Edomite tribes, and perhaps even from his father-in-law, Ethbaal, and the kings of Hamath and Arpad.