Mismatch

"Hide your wives and daughter; hide the groceries too.
The great nations of Europe comin through."

The irony in this phrase is that the singer expresses Europe as "great nations" but such nations of glory are also cautioned. Nations of such wealth were still stealing, and still raping. The irony is that Europe is supposedly more civilized but the fact that less civilized persons have to hide their families and their groceries are the satire imposed. 

"There's pictures in a museum, some lines written in a book
but you won't find a live one, no matter where you look."

There is no irony present in this part of the song. The author wants to exaggerate the fact that the conquerors write history. He wants to mention the forgotten memories and cultures of the indigenous personnel, especially by mentioning that even the birds were extinct. 

"Church told him were gay,
soooooooooooooo
he had them torn apart by dogs on religious grounds they say
the great nations of Europe were quite holy in their way."

The irony here is that the church should symbolize an authority, but an authority of good, an insituticon to spread the word of god. The complete opposite is mentioned in the song, an insituiotion that compels their "loyal disciples" to spread the word of god by killing and discriminating. The exact opposite of the word of god. "The holy way" of Europe is in fact not holy, its the complete opposite of holiness.