
östlich
east of
Indicates the location or position in the east or in an easterly direction from a reference point.
Frankfurt an der Oder liegt östlich von Berlin.
Frankfurt an der Oder is east of Berlin.
eastern / east of
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east of
Indicates the location or position in the east or in an easterly direction from a reference point.
Frankfurt an der Oder liegt östlich von Berlin.
Frankfurt an der Oder is east of Berlin.

eastern
Indicates the direction of origin, usually in relation to wind that comes from the east.
Bei östlichem Wind wird es meist kälter.
With an eastern wind, it usually gets colder.
The adjective 'östlich' (eastern/east of) is derived from the noun 'der Osten' (the east). The ending '-lich' is often used to form adjectives from nouns that describe belonging or a characteristic.
Der östliche Teil des Landes ist weniger dicht besiedelt.
The eastern part of the country is less densely populated.
'Östlich' (east of/eastern) describes a static position. If you want to express movement in that direction, you use the preposition 'nach' and the noun, for example 'nach Osten fahren' (to drive/travel east).
Das Dorf liegt östlich des Flusses.
The village lies east of the river.
To indicate a position relative to another place, 'östlich' (east of) is almost always used with the preposition 'von' and the dative.
Leipzig befindet sich östlich von Halle.
Leipzig is located east of Halle.
In connection with the weather, 'östlich' (eastern) is used almost exclusively to describe wind direction. In that case, people speak of 'östlichem Wind' (eastern wind).
Für morgen ist kalter, östlicher Wind vorhergesagt.
Cold eastern wind is forecast for tomorrow.
east
Der Osten is a noun and refers to the eastern part of an area. Östlich, by contrast, describes a location in the direction of the east, usually in relation to a stated place. Thus, someone lives im Osten einer Stadt (in the eastern part of a city) or östlich eines bestimmten Punktes (east of a specific point).

Mia wohnt östlich des Stadtzentrums.
Mia lives east of the city center.
Mia wohnt im Osten der Stadt.
Mia lives in the eastern part of the city.