huh... so you got this sentence from a dictionary example? 숨을 못 쉬도록 빨리 뛰었어요. I also have to agree that the sentence is awkward, and I guess in some odd way it can be translated as "I ran until I couldn't breathe", but it sounds not correct. I can't exactly explain why...

숨을 못쉬도록 빨리 뛰었어요'i think this sentence is awkward..and 숨을 못 쉴 정도로 빨리 뛰었어요 is natural. 저는 토하고 싶을 정도로 많이 먹었어요 is also awkward sentence cuz it means, u eat too much to throw out. so,저는 토할 정도로 많이 먹었어요 or저는 너무 많이 먹어서 토 할뻔했어요.is correct

Your understanding is correct. -도록 is similar to "so that", "so ... that ...", or "enough to". In addition to indicating a purpose or intention, It can mean a result or degree of an action, similar to 정도로. However, -도록 is much more natural and in wider use. 정도로 implies a serious comparison and is not suitable for any figurative or idiomatic speech. -도록 is primarily a verb ending form (conjugation), but it's sometimes used like a particle (조사 in Korean) - but this happens in a fairly limited number of cases. Your examples are okay, but they don't seem to be the most natural way to say it. 1) 숨을 못 쉬도록 빨리 뛰었어요. => 숨이 차도록 빨리 뛰었어요 is more common. (숨이 차다 = idiom for "breathe hard"). 2) 저는 토하고 싶을 정도로 과식을 했어요 => 너무 먹어서 토할 것 같았어요 is more natural. Here are some common idiomatic phrases using -도록 to indicate the extent or degree of something. - 밤이 새도록 [or 밤새도록, 날이 밝도록] 놀았다. Partied all night long. - 죽도록 고생했다. Went to hell and came back (busted myself). - 배가 터지도록 먹었다. Ate like a pig (till my stomach busted). - 미치도록 보고 싶었다. Went crazy from missing you/someone. - 발이 닳도록 돌아다녔다. Ran around till my feet wore out. - 입이 마르도록 떠들었다 [잔소리했다]. Talked [nagged] myself hoarse (till my lips were dry). - 눈이 빠지도록 기다렸다. Waited until my eyes popped out. - 손이 발이 되도록 빌었다. Begged on all four (using hands and fee and everthying). and here are examples of particle-like usage - they appear only in some special phrases) - 평생토록 = 한평생 동안; 영원토록 = 영원히; 종일토록 = 하루 종일; - 이토록, 저토록, 그토록 = to this, that, such an extent. (It becomes 토록 in these words for pronunciation-related reasons, We don't say 평생도록 or 이도록)

H.S.'s explanation is perfect. To reiterate, " '~도록' is something like, "so that it can be achieved or becomes reality" when coupled with verbs in expressions like, "할수 있도록", "될수 있도록", etc. "~정도로" has the word "정도", which means a certain "degree" or "level". So it has the meaning, "up to a certain level", "to the extent to which", "until reaching a degree of...", etc. Despite some similarity in sound, I do not think they are related in anyway, and are not interchangeable.

u can use '~도록' with verb like 그 일이 성공 할 수 있도록 최선을 다하다.=i ll try my best to sucess this project. it contains the chracter of achieving goals or aim. ~정도로 means,as much as or the level,degree of sth. 나는 밥을 못먹을 정도로 어릴때 가난했다=when i was young,i was very poor as much as i couldnt have a meal. well, my english must be incorrect but plz understand and i hope my answer is helpful for u . p.s.im native S. Korean.