For hanging and hang out, it depends on sentence stress. As you may know, most words in English have both strong and weak forms, so there are two different pronunciations. If a word has stress in the sentence, we pronounce the strong form. If it doesn't have stress, we pronounce the weak form.
Hanging would be pronounced as /'hæŋi:ŋ/ if it has stress in the sentence.
Example:
a: Is the clock sitting on the desk?
b: No, it's /'hæŋi:ŋ/ on the wall.
However, if hanging only has normal stress, it would be pronounced as /'hæŋɪŋ/.
If hanging is unstressed, it would be pronounced like /'hæŋɪn/
Hang out is usually pronounced as its weak form - /hæŋaʊt/ <- note how the two words have blended together. However, it would be pronounced as /hæŋ aʊt/ if the speaker were correcting someone using the phrase 'hang out.'
Long, song, and lung are content words and will almost always be pronounced with stress in sentences.