Invasion, incursion, raid, inroad are comparable when meaning an entrance effected by force or strategy.
Invasion basically implies entrance upon another's territory with such hostile intentions as conquest, plunder, or use as a basis of operations. In nonmilitary use it may imply encroachment, trespass, or an intrusion that involves an aggressive or hostile purpose.
Sometimes it implies no more than entrance with or as if with a rush by a horde or crowd.
Incursion, especially in military use, carries a stronger connotation of suddenness, unexpectedness, or haste than invasion; it often also suggests an immediate end and a quick withdrawal when the end is achieved. In its extended sense incursion applies chiefly to an invasion in large numbers of something dreaded or harmful, undesirable, but not necessarily inimical.
Raid, frequent in military use for a swift, sudden invasion (as of cavalry or of air forces) may or may not suggest more preparation, more strategy, and more fury in attack than incursion, its close synonym.
In international law, however, raid is applicable specifically to an incursion of armed forces that are unauthorized or unrecognized by any state into a country that is at peace; thus, an incursion of armed persons on one side of a border or boundary line into the adjoining country for a predatory or hostile purpose is technically a raid. In its extended use raid applies to a sudden descent or a flurry of activity intended usually to obtain the use, control, or possession of something; thus, officers of the law conduct a raid upon a gambling resort or a place where liquor is illicitly made or sold to obtain evidence and arrest offenders.
Inroad may apply to a sudden hostile incursion or a forcible entering, but the term is also applied to an invasion that involves encroachment or advance especially at the expense of someone or something.