A DSc is a 'Doctor of Science'. Some universities/departments award DSc's instead of PhDs - essentially they are the same thing. An Honours Degree is a type of first degree, eg BSc (Hons) or BA (Hons). Most UK degrees are honours degrees.
An Honorary PhD, Doctorate or Masters degree is awarded by a university to high achievers who have some connection with the university. People who receive them are usually very senior academics, industrialists and community workers or famous artists, authors and celebrities. The reason for awarding the degree is usually to give the university some publicity or to honour the person concerned for their contribution to society or their field.
People with honorary degrees can use the title if they want, but most do not.