Jamieson, Fausset and Brown on Obadiah 1:16

16. ye ... upon my holy mountain--a periphrasis for, "ye Jews" [Maurer], whom Obadiah now by a sudden apostrophe addresses. The clause, "upon My holy mountain," expresses the reason of the vengeance to be taken on Judah's foes; namely, that Jerusalem is God's holy mountain, the seat of His temple, and Judah His covenant-people. Jr 49:12, which is copied from Obadiah, establishes this view (compare 1Pe 4:17).

as ye have drunk, &c.--namely, the cup of wrath, being dispossessed of your goods and places as a nation, by Edom and all the heathen; so shall all the heathen (Edom included) drink the same cup (Psa 60:3; Is 51:17, 22; Jr 13:12, 13; 25:15-33; 49:12; 51:7; La 4:21, 22 Na 3:11; Ha 2:16).

continually--whereas Judah's calamity shall be temporary (Ob 17). The foes of Judah shall never regain their former position (Ob 18, 19).

swallow down--so as not to leave anything in the cup of calamity; not merely "drink" (Psa 75:8).

be as though they had not been--not a trace left of their national existence (Job 10:19; Psa 37:36; Eze 26:21).