"While you don't mention exactly where you grew up, if your
grandmother routinely told you to "redd up" your room, there's a
statistical probability that either you were living in, or your
grandmother was from, Pennsylvania. "Redd up," meaning "to clear or
clean up," arrived in America with immigrants from Scotland and
northern England, and while Scots settled all over the eastern US, the
phrase seems to be most commonly heard today, for some reason, in
Pennsylvania.

The root of "redd" (which by itself means "to clear or clean") seems
to be a combination of the Middle English and Scots dialectical word
"redden" (meaning "to free or clear an area") with another Middle
English word, "reden," meaning "to rescue or free from." The same
tangle of roots gave us the word "rid," and is closely related to the
word "ready." And none of this, by the way, has anything to do with
the color "red."

from the Word Detective: http://www.word-detective.com/121800.html

Frank Reid