I use premium sleeves.
First card-width drawer: Heroes, w/ their character cards and variants
Second card-width drawer: The rest of the heroes, except void guard, also w/ their character cards and variants
Third card-width drawer: Villains, w/ their character cards and variants
Fourth card-width drawer: Environments, Void Guard, and OblivAeon missions/rewards
Larger drawer, front well: Tokens and dice
Larger drawer, second well: Other OblivAeon decks besides the missions/rewards, plus the five Vengeance decks
Larger drawer, third well: The ten Villains decks
Larger drawer, fourth well: OblivAeon-specific tokens, plus the OblivAeon oversize cards
Wide, top drawer: Rule books and a menagerie of oddities: Sentinel points, pins, old tracker cards, signed cards, and others.
It occurs to me that I've failed to include the Vengeance and Villains character cards in the collectors case. I'll need to add those into the fourth well. I haven't sleeved any of the oversized cards yet. Not sure whether I will or not.