südöstlich
southeastern
Describes a location, direction, or orientation that lies between south and east.
Das Dorf liegt südöstlich der Hauptstadt, direkt am Fluss.
The village is located southeast of the capital, right by the river.

southeastern
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southeastern
Describes a location, direction, or orientation that lies between south and east.
Das Dorf liegt südöstlich der Hauptstadt, direkt am Fluss.
The village is located southeast of the capital, right by the river.

'Südöstlich' (southeastern) is composed of the compass directions 'Süd' (south) and 'Ost' (east). This pattern works for all intermediate compass directions, such as 'nordwestlich' (northwestern) or 'südwestlich' (southwestern).
Der Wind kommt heute aus südöstlicher Richtung.
The wind is coming from a southeasterly direction today.
'Südöstlich' (southeastern / southeast) is very often used in the combination 'südöstlich von + [place]' to indicate a relative position. The place is in the dative.
München liegt südöstlich von Frankfurt am Main.
Munich is southeast of Frankfurt am Main.
'Südöstlich' (southeastern / southeast) can be used as an adverb and then remains unchanged. If it comes before a noun as an adjective, it must be declined like any adjective.
Wir fahren südöstlich.
We are driving southeast.
southern / south of
'südlich' and 'südöstlich' both describe a location or direction in the southern area. 'südlich' is more general and only says that something is in the south or points south. 'südöstlich' is more precise and means a direction between south and east. That is why the words can be confused if you are only thinking roughly of 'south'. For a simple location in the south, you say 'südlich'. If you want to say more precisely that something is also toward the east, 'südöstlich' fits better.

Wir besuchen morgen ein Dorf südöstlich der Stadt.
Tomorrow we are visiting a village southeast of the city.
Heute trainiert die Gruppe südlich vom Stadion.
Today the group is training south of the stadium.