Your book's right about the first. 'I made him go' is either a reported command, or an account of physically intervening. 'He never does his homework because Facebook is too distracting. So I sat in the same room and made him do it.'
So 'I made him...' (he didn't want to); I let him...' (he did want to). 'Had him....' and 'Got him to...' are in between those extremes, but I wouldn't rank them - perhaps, if forced, I'd make 'had him...' more urgent than 'got him to...' (which has an implication of cajoling or asking a favour).
Student or Learner