In Japanese, there are two ways to express southeast: 東南 "tounan" = "east-south" or 南東 "nantou" = "south-east". However, they have different uses. Use "east-south" if you're talking about a particular location, e.g., Southeast Asia = 東南アジア. When talking about a particular direction, use "south-east": southeasterly wind = 南東の風.
Miura, Akira. Essential Japanese Vocabulary, Tuttle Publishing.