I know that the 1st one is a passive voice, 2nd is a state of the door (which is opened) and opened here is an adjective, right? But when do we use the 3rd one? I'm pretty sure that I've seen it somewhere but can't get the area of usage.
... door is opened
You are right, opened is a past participle, which is used after is to indicate passive voice. An example sentence might be
If the door is opened, the alarm will sound.
Note that, for some verbs, the past participle has the same form as the corresponding adjective, for example broken. You can't assume that something that looks like a past participle after is, actually is a past participle.
... door is open
Here, open is used as an predicative adjective - after the verb. here is an example sentence:
The door is open.
... door open
Here, open is used as an attributive adjective. Attributive adjectives usually go before the noun:
The open door shifted back and forth in the wind.
In some cases, an attributive adjective can go after a noun, as in this sentence.
He held the door open as I approached.
This article explains describes some situations where an attributive adjective can go after the noun.