Many words cannot directly be translated between languages, and '오빠' does not exaclly mean the same things that 'brother' can in English does. If you find it less disgusting, think of the meaning as 'older male'. You might think it's strange that there's not a separate word to distinguish a blood brother, but age is a very important element of status in Korean culture. Until recently, even having a boyfriend might have been considered shameful - perhaps that's one reason why there's no more proper word you can use meaning 'boyfriend' in the vocative case!

How that is weird? There are some words to call someone order/younger then you instead of calling their names. So if you are a female and you have a order bother, you call him the same way. Simply because he is older then you. However when you introduce your older bother, you can use 친오빠. It means one's own brother. 누나/오빠 is just the most basic way to call someone order then you. Some girls call their boyfriend 오빠 because their boyfriends are order then them. Is not like darling, sweetie, hon, etc. What do you thinking?

It's a little hard to answer your question, because we don't know exactly where you're coming from. How does it work in your own culture? One teacher here has explained the "oppa" issue fairly well in this post: http://www.italki.com/entry/437405 I wonder why you've chosen to read incest into these expressions, but really, it's not the case. It's just a mode of expression. In English-speaking culture, yes it is a little odd to call your partner "brother" or "sister", but that's just our own way of looking at it. The closest thing we have to this is, if you have a sister, it's possible for her to call your girlfriend "sis(ter)". Still, "sis" and "bro" are casual forms of address.