What is the correct ATC phraseology in the US for an immediate - no delay takeoff?
The FAA AIM and ATC (7110.65) documents don't mention the ICAO equivalent. But I found it in the US AIP:


  34.1 (...) At times a clearance may include
  the word “IMMEDIATE.” For example:
  “CLEARED FOR IMMEDIATE TAKEOFF.” In
  such cases “IMMEDIATE” is used for purposes of air
  traffic separation. It is up to the pilot to refuse the
  clearance if, in the pilot’s opinion, compliance would
  adversely affect the operation.