I am the father of seven children.
You are the major scale, and your seven children are the individual tones of the scale expressed in solfege. A "harmonious family" indeed!
My first son is a man of action.
DO -- the verb "do"
My second son's reputation is concerning.
RE -- in correspondence, the abbreviation "Re:" for "regarding", a synonym of "concerning"
My third son shuttles between London and Leeds in his job.
MI -- the M1 motorway connecting London and Leeds
There is nothing at all I can say about my fourth son.
FA -- "Sweet F.A." (Fanny Adams), a slang expression meaning "nothing".
Surya, my fifth son, is a bright chap.
SOL -- i.e. the sun; Surya is the Hindu solar deity
My sixth son works in Hollywood.
LA -- abbreviation for Los Angeles
My seventh son is known for his great strength.
TI -- abbreviation for Titanium, the strongest metal