
eigenartig
strange
Odd, peculiar, or weird; deviating from the norm and therefore causing surprise or puzzlement.
Er hat einen sehr eigenartigen Humor, den nicht jeder versteht.
He has a very strange sense of humor that not everyone understands.
strange / characteristic
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strange
Odd, peculiar, or weird; deviating from the norm and therefore causing surprise or puzzlement.
Er hat einen sehr eigenartigen Humor, den nicht jeder versteht.
He has a very strange sense of humor that not everyone understands.

characteristic
Characteristic or specific to a particular person, thing, or group; showing a special distinctive quality.
Die dem Barock eigenartige Prachtentfaltung zeigt sich in dieser Architektur besonders deutlich.
The splendor characteristic of the Baroque is especially clear in this architecture.
The word is made up of 'eigen' (own) and 'Art' (kind/type). It describes something that has its 'own way' or 'own kind.' This explains both meanings: something with its own way can be strange (m01) or characteristic (m02).
Sein Kleidungsstil ist ziemlich eigenartig.
His style of dress is quite strange.
The meaning 'seltsam' (strange) is more common in everyday language and often refers to people, behavior, or situations. The meaning 'charakteristisch' (characteristic) is more formal and is often used in descriptive texts, e.g. about art or science.
Das Essen hatte einen eigenartigen Nachgeschmack.
The food had a strange aftertaste.
In the meaning 'seltsam' (strange), the adjective is often connected with sensory perceptions or people. Typical phrases are 'ein eigenartiger Geruch' (a strange smell), 'ein eigenartiges Gefühl' (a strange feeling), or 'ein eigenartiger Mensch' (a strange person).
Als ich den Keller betrat, hatte ich ein eigenartiges Gefühl.
When I entered the basement, I had a strange feeling.
In the meaning 'charakteristisch' (characteristic), 'eigenartig' (characteristic) often appears with a dative object that indicates for whom or what something is typical. The structure is: 'etwas ist [Dativ] eigenartig' (something is characteristic of [dative]).
Die besondere Farbgebung ist diesem Maler eigenartig.
The special use of color is characteristic of this painter.
own / peculiar
Eigen and eigenartig can both mean that something seems odd. In this use, eigen is regionally or stylistically marked and may therefore sound unfamiliar. Eigenartig is the generally understood choice when a deviation causes surprise.

Sein Verhalten kam mir eigenartig vor.
His behavior seemed strange to me.
Sein Verhalten kam mir eigen vor.
His behavior seemed peculiar to me.