While reading fanfics, I noticed that a handful of authors don't know how to use 오빠 (oppa), 언니(unnie), 형 (hyung), or 누나 (noona).

This is the polite informal way of speaking.  

When you speak informal, you can say 야 (yah) after somebody's name to call them.  To older friends, this is a BIG NO-NO.  They will seriously get mad at you. Or call you very disrespectful.  Or scold you and tell you to stop joking around.

So you use 오빠, 언니,형, or 누나. 

Girls: to older guys- 오빠; to older girls- 언니

Guys: to older guys- 형; to older girls- 누나

Anyone younger than you are all 동생 (dongsang).

This (오빠, 언니, 형, 누나) is more or less a title.  Like the words president, governer or doctor is a title.  Ignoring this title is VERY BAD. I can never emphasize this enough.  It's like saying "Hey! You!" to a teacher. 동생 is never a title though. Just a person who is younger.

Siblings also call their brothers and sisters by this title. When they tell other people about their siblings, they add 친 (chin) before the title.  To say that the person is their biological sibling.  This also applies to 동생.