Order, arrange, marshal, organize, systematize, methodize are comparable when they mean to put (a number of persons or things) in proper place especially relatively or to bring about an orderly disposition of individuals, units, or elements that comprise (a thing).
Order is somewhat outmoded when the idea of putting in a definite order is to be expressed; it more usually implies a straightening out and may connote either the elimination of friction or confusion, often with resulting peace or harmony, or the imposition of a fixed and rigid discipline.
Arrange is more often used than order where the idea of setting in proper sequence, relationship, or adjustment is uppermost. The word often implies a notion of what is orderly, fit, suitable, or right and a placing of things in accordance with this notion.
Often the term implies a determination of the way in which the things are disposed by an end in view and then suggests careful management or manipulation.
Marshal usually connotes generalship and implies assemblage and arrangement either for ease or advantage in management (as under stress) or for effectiveness in display or exhibition.
Organize implies an arrangement in which all persons or things are so related to each other that they work as a unit, each individual having his or its proper function or duty.
Systematize implies arrangement according to a definite and planned scheme; thus, one systematizes one's daily work when one reduces it to routine order.
Methodize differs from systematize in suggesting the imposition of orderly procedure rather than of a fixed scheme; thus, one can methodize one's work without giving it the character of routine.