In all likelihood, the SEC with 9 eligible teams won't fill a Group of 6 bowl ( 1 team in playoffs, 2 others in NY6, and one in Citrus does that). 2 teams in the playoffs would probably mean only 1 in the Sugar Bowl (I doubt Florida makes it but is a lock for the Citrus).

How does the league choose the odd game out?

Assumptions: Oregon over Utah in PAC championship, Ohio St over Wisconsin in B1G championship, Clemson over Virginia in ACC championship, Oklahoma over Baylor in XII championship

If LSU loses an incredibly close championship game to Georgia, I could see LSU still getting the #4 spot. With 2 CFP teams (guessing on some other matches):
Peach: #3 Georgia vs. #2 Clemson
Fiesta: #4 LSU vs. #1 Ohio St
Sugar: Alabama vs. Oklahoma
Orange: Florida vs. Virginia / Virginia Tech
Rose: Oregon vs. Penn St
Cotton: Utah vs. Memphis

If LSU wins:
Peach: #1 Ohio St vs. #4 Oklahoma
Fiesta: #2 LSU vs. #3 Clemson
Rose: Oregon vs. Penn St
Sugar: Alabama vs. Baylor
Orange: Georgia vs. Virginia / Virginia Tech
Cotton: Utah vs. Memphis

If Georgia has blowout win:
Peach: #1 Ohio St vs. #4 Oklahoma
Fiesta: #2 Clemson vs. #3 Georgia
Rose: Oregon vs. Penn St
Sugar: LSU vs. Baylor
Orange: Alabama vs. Virginia / Virginia Tech
Cotton: Utah vs. Memphis

If Utah wins the Pac12 championship game, there will be much expectation to put them in the playoffs.