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.

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.
western
'westlich' and 'östlich' both describe a location or direction. They are opposites: 'westlich' means in the direction of west or west of a place, while 'östlich' means in the direction of east or east of a place. Both words are often used with 'von' when naming a reference point. They are easy to mix up because they are built the same way and both describe cardinal directions. So always pay attention to the reference point: if the place is to the left on a standard map, it is 'westlich'; if it is to the right, it is 'östlich'.

Er sucht ein Hotel, das östlich vom Bahnhof liegt.
He is looking for a hotel that is east of the train station.
Das kleine Dorf liegt westlich von München.
The small village is located west of Munich.