Fast bowlers James Anderson (40) and Josh Tongue (25) have been rested while vice-captain Ollie Pope (25) has been ruled out of the rest of the series after dislocating his shoulder, which requires surgery.
With Pope not in the squad, Harry Brook (24) will be promoted to number three.
Moeen came out of retirement for the first test but the spinner injured his finger, sitting out the second encounter at Lord's.
Wood was not picked for the first two tests and England will welcome his fiery pace while Woakes' all-round ability will give the hosts depth in their batting line-up.
Anderson is England's leading wicket-taker in tests (688) but he struggled to make an impact in the series with just three wickets in the first two matches.
Tongue made his test debut against Ireland last month where he impressed with a five-wicket haul in the second innings and made his Ashes bow at Lord's, where he took five in two innings.
England XI: Zak Crawley, Ben Duckett, Harry Brook, Joe Root, Jonny Bairstow, Ben Stokes (captain), Moeen Ali, Chris Woakes, Mark Wood, Ollie Robinson, Stuart Broad.
