Obedience means that units are compelled to obey orders. However, depending on the unit's relative Loyalty or intelligence, they may voice their diagreement or outright disobey the orders if they believe the order goes against higher orders or their Ruler's interests Erf-b1-p005. Disobedience may cause the unit to disband, but a clever and resourceful unit like Wanda can carry out a lot of stuff under the table.
Orders enforced by Obedience are not limited to ones involving strategy and combat. In fact, nearly any command comes under its purview: A superior can order a unit to laugh, cry, slap themselves, strip naked and do whatever their imaginations demand. That abusing a underling's obedience in any manner might be wrong is an alien concept to the people of Erfworld. Erf-b1.5-p044