Short answers, pulled from the story.
Military organization is the structuring of a state's armed forces to provide the military capability that national defense policy requires. Formal military organization uses hierarchical forms because this structure, which came into widespread use with the Roman Army, allows a single officer's intent to be translated into coordinated action across large numbers of troops.
A command is a collection of units and formations under a single officer, functioning as an administrative and executive strategic headquarters. A formation, such as a division or brigade, combines different arms and services into a balanced combat force. A unit is homogeneous, drawing its personnel predominantly from a single arm or branch of service, with self-contained administrative and command functions.
The modern Corps was first introduced in France around 1805 by Napoleon as a more flexible tactical grouping of two or more divisions during the Napoleonic Wars.
In most navies a squadron is a formation of several ships; in most air forces it is a unit; in the U.S. Army it is a battalion-sized cavalry unit; and in Commonwealth armies it is a company-sized sub-unit. Different armed forces and even different branches within the same armed force may use the same name to denote different types of organizations.
A table of organization and equipment, or TOE, is a document published by the U.S. Army Force Management Support Agency that prescribes the organization, manning, and equipage of units from divisional size downward, including the headquarters of Corps and Armies. A general TOE applies to a type of unit, such as infantry, rather than to a specific named unit.
Within NATO, a Joint Task Force is a temporary grouping that includes elements from more than one armed service. A Combined Task Force is a temporary grouping that includes elements from more than one nation. A Combined Joint Task Force includes elements from more than one armed service and more than one nation simultaneously.