If we're talking about war, then to invade means to physically enter another's country to wage war. To aggress is to initiate an argument but stops short of invasion, although it may eventually lead to an invasion. If the US sends warships to sit off the coast of a country, it is not an invasion, but it could be said to be showing aggression. As a word, "aggress" is hardly ever used.

To invade is to move your army into another country's land. Or to move within another's "space" - invade someone's privacy. I'm not sure aggress is a word. To be aggressive is to threaten violence or action or actually carry it out.