An indestructible creature cannot be destroyed. Only three things in Magic cause destruction: 1) effects that use the word "destroy", 2) lethal damage marked on a creature, 3) damage to a creature from a source with deathtouch. Those are the things indestructible helps against.
Your Angelic Overseer
lives. Be careful, though! If you lose control of your last human during that same turn and thus you angel loses the indestructability, the still lethally damaged Overseer will be destroyed. Marked damage stays on permanents until it gets removed in the cleanup step or until an effect removes it (regeneration, totem armor).