Do skill check re-rolls include dice gained from spending clue tokens?
Reroll all 4 dice.

It's important to do things in the right order though.  Using the cigarette case and then clues results in fewer total rolls.

This is clarified in the FAQ contained within the Dunwich Horror rules


  Q: How does a re-roll work? Can you re-roll only the
  skill dice that you have before spending Clue tokens, or
  can you re-roll all the dice you’ve rolled on a given
  check, including the extra dice gained from spending
  Clue tokens?
  
  A: You re-roll all the dice you’ve rolled for the skill
  check so far, so you can re-roll dice gained from spending
  Clue tokens as long as you spend your Clue tokens
  before using your re-roll.