Hardy is playing Col. Rick Flagg jr. a super tough U.S. Air Force special operations officer. The original field commander of the Squad, he is a strong willed character that is as close to a white knight that the Squad has. Granted, he also is willing to make the tough calls as a military man.
Jai Courtney is playing Captain Boomerang, Digger Harkness. Boomer is a thief, inventor and hired thug who is a savant when it comes to combat with the boomerang. In the comics he started out as a spokesman for a company that made toy boomerangs, but turned to crime. Digger is a low life misogynist, racist worm... But he is a survivor. He looks out for himself and no one else.
Smith is Floyd Lawton, aka Deadshot, a master sniper and maybe the greatest assassin in the world after Deathstroke. Lawton has a complex family history that's sort of an inverse of Bruce Wayne. Wealthy background, but he saw his parents kill each other. He has a strange death wish, but he is also casually cool, level headed... And ruthless. He and Flagg go at it quite a bit.
Cara Delevigne is June Moon aka Enchantress. A powerful sorceress the personality is spit between mousy June and Enchantress. The more power she uses the less control of her body June has and the Enchantress personality takes over.
The others like Joker and Harley I am sure you already know.