Since Obadiah's concern was Jerusalem, and since it seems likely that he lived in Judah, the original audience that received his prophecy may also have been the residents of Judah.
Obadiah wrote to announce coming divine judgment on Edom and to give the people of Israel hope by reminding them of the future that God promised them.
"Prophetic oracles against foreign nations, though full of the language of doom, are also implicitly messages of hope for God's people. Such oracles look forward to a time when the predicted demise of the nation under attack will open the way for the restored, purified Israel to blossom once again as the flower of all God's plantings.
"Obadiah's message fits this pattern and in some ways even typifies it."7
"In a sense Obadiah is a miniature profile of the message of all the writing prophets."8
"Edom . . . was tenaciously and rather constantly hostile from beginning, i.e., after the exodus, to end, i.e., after the exile. This factor would itself be enough to cause such a small nation to receive such regular, even prominent mention in prophetic oracles against foreign nations. But Edom's prominence as an enemy was additionally noteworthy because of its historical position as a brother nation to Israel (Gen 25). There are, then, at least three factors that made Edom so prominent among Israel's enemies that it could sometimes function virtually as a paradigm for all of them: (1) the sheer chronological length of its enmity as alluded to in Ezek 35:5; (2) the consistency and intensity of its enmity (as in Obad 10-14); (3) the treasonous' nature of its enmity (as in Amos 1:11). No other nation quite shared these characteristics.
". . . of the ancient non-superpowers (i.e., leaving aside Egypt, Assyria, and Babylon) Edom is the subject of more separate oracles against foreign nations (seven [i.e., Isa. 21:11-12; Jer. 49:7-22; Ezek. 25:12-14; 35; Amos 1:11-12; Obad.; Mal. 1:2-5]) and more brief or passing hostile references (four [i.e., Isa. 11:14; Jer. 25:21; Lam. 4:21; Joel 3:19]) in the prophetical books than any other nation."9
"The Edomites played such a consistently adversarial role in Israel's history that the prophetic literary category of oracles against foreign nations' was bound to include predictions of judgments against Edom. Edom, indeed, becomes in the OT a kind of metonymy for hostile nations.'"10
Edom is the subject of the little Book of Obadiah as Assyria is of the larger Book of Nahum. The New Testament does not quote from or allude to the Book of Obadiah.