/ø/ is generally found at the end of a syllable. It's the sound in "deux (2), feu, bleu, heureux". /œ/ is generally found in a closed syllable, meaning there's a consonant following it. It's in "neuf (9), peur, soeur, oeuf". The same thing (closed vs. open syllable) happens with the "o" as well ("pot" vs. "porte"). I hope this helps! :)

/ø/ is used in "feu", it's a close-mid oral rounded vowel /œ/ is used in "fleur",, it's an open-mid oral rounded vowel Interestingly, you can compare "jeune" (/œ/) and "jeûne" ( /ø/ ) The lips when you produce the sound /ø/ in "jeûne" are more closed than when saying /œ/ in "jeune". You may find this page interesting: http://en.wikipedia.org/wiki/French_phonology