Can I use "which" after the subject when it's insect or animal like this sentence below?
"The owl is bird which is included in nocturnal animal."
And is it right to put "the" to indicate every species included in such owl as white owl, brown owl, etc?
Yes, it is.
However, I would rephrase the sentence, make it simpler: "The owl is a nocturnal bird."
And about "the": if every species of owl is nocturnal, then it is all right. If not all are, you should mention it: "The owl is a nocturnal bird, except the _____ and the _____ owls, which can be seen both at night or during the day." (just an example, not that I actually know anyhting about owls)
Please be aware that I'm neither a native English speaker nor a teacher.