ostwärts
eastward
Indicates movement or direction toward the east.
Wir fuhren mit dem Zug immer weiter ostwärts in Richtung der polnischen Grenze.
We traveled by train farther and farther eastward toward the Polish border.

eastward
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eastward
Indicates movement or direction toward the east.
Wir fuhren mit dem Zug immer weiter ostwärts in Richtung der polnischen Grenze.
We traveled by train farther and farther eastward toward the Polish border.

The ending '-wärts' always indicates a direction. It can be attached to compass directions ('nordwärts' — northward, 'südwärts' — southward, 'westwärts' — westward) or other place-related words ('heimwärts' — homeward, 'abwärts' — downward).
Die Vögel fliegen im Herbst südwärts.
The birds fly southward in autumn.
As an adverb of direction, 'ostwärts' (eastward) usually comes after the conjugated verb and any objects. It answers the question 'Wohin?' (Where to?).
Die Expedition bewegte sich langsam ostwärts durch den Dschungel.
The expedition moved slowly eastward through the jungle.
The word 'ostwärts' (eastward) is often used in written language, in literary texts, or in more formal travel descriptions.
Der Roman beschreibt eine lange Reise ostwärts.
The novel describes a long journey eastward.
'Ostwärts' (eastward) is almost always combined with verbs of movement. Typical examples are 'fahren' (to drive/travel), 'gehen' (to go/walk), 'fliegen' (to fly), 'ziehen' (to move/migrate), or 'reisen' (to travel).
Die Familie fuhr mit dem Auto ostwärts in den Urlaub.
The family drove eastward by car for their vacation.
eastern / east of
'östlich' and 'ostwärts' both have to do with the direction east. 'östlich' usually describes the location of something: a place is in the east or east of another place. 'ostwärts', on the other hand, describes movement toward the east. So with 'östlich', the question is more: Where is something located? With 'ostwärts', the question is: Where is someone or something moving? The words are easy to confuse because both name the same compass direction, but they fit into different types of sentences.

Nach der Pause fährt der Zug weiter ostwärts.
After the break, the train continues eastward.
Das Dorf liegt östlich von München.
The village is east of Munich.