tarnal (TAR-nuhl) - adj., damned.
passel (PAS-uhl) - n., an indeterminately large quantity or group.
Both of these are Americanisms. Tarnal is a dialect variation on eternal, as in eternal damnation, and like tarnation is a regional usage attested in the American colonies from the 18th century, before Independence. Passel is slightly later and more widespread -- it's an alteration of parcel dating from around 1830. Both are in the colloquial register, and the former counts as very mild cussing.
I told Jeb that if he keeps up like this, he'll have a passel of troubles, but the tarnal fool didn't listen to a word I said.