I look at it as Gay being the starter at SF and Omri being his backup. With Karl looking to theoretically play Rudy at the PF a lot that means a lot of minutes for Omri. Those two are key players for the Kings.
Mbah a Moute and Butler are much more situational. A versatile, defense-first player was something Karl was lobbying for before the draft.
That would Mbah a Moute. He's had success guarding SGs, SFs and PFs and even some PGs. He'll be a guy that Karl calls on when needed. I think Butler was brought on primarily for two things - to be a solid vet/good locker room presence and to be insurance in case of injury. Essentially he'll be the third SG and SF which will be an important role during a long season.
The Kings obviously need a 3rd PG and I think they need one more big, ideally a PF with some offensive capability. Josh Smith, Darrell Arthur and Kevin Seraphin would be my top picks but I don't think the Kings have the capspace or role to bag them.