Can {Oath of the Ancient Wood} trigger heroic ?
No it would not trigger heroic. Because when its targets your creature, it's a permanent, not a spell.
Shouldn't it trigger when its cast? Not later on, but when it enters the battlefield?
"Enters the battlefield" is part of the spell's resolution, so since the +1/+1 ability doesn't occur until it enters, at that point Oath is a permanent, not a spell, and thus can not trigger heroic.