Origin and meaning of "damn straight"

Etymonline reports that straight to mean "true, direct, honest" is from 1520s.

The third entry in NOAD lists the meaning of straight as

3 not evasive; honest : a straight answer | thank you for being straight with me.

Note the first example: a straight answer. The comment "damn straight" emerges directly from this kind of construction. It is always used in response to a statement that the speaker strongly agrees with, and is an acknowledgement of the candor and frankness of the original statement.

But there's more. It also parallels a similar possible response: "Damn right" (meaning "You're damned right.") and means the same thing. These two are interchangeable and probably merged in meaning; one often hears "You're damn[ed] straight," completing the merge. So in this sense "straight" and "right" mean pretty much the same thing. The actual meanings of "straight" and "right" are less important than the emphatic note of strong agreement.