The 24-year-old Archer took 20 wickets in the World Cup and was not expected to face Australia until later in the five-test series due to a side strain picked up during the tournament, but he returned to action for Sussex on Friday night.
Stokes, who was man of the match when England beat New Zealand in the final, returns to the leadership role he was stripped of following his part in a late-night brawl in September 2017. He missed that winter's Ashes series as a result before being cleared on a charge of affray in Bristol Crown Court last summer.
Ten of the 11 players who defeated Ireland in a rollercoaster test win at Lord's this week were included Saturday in the 14-man squad, joined by Stokes, Archer, Jos Buttler and Jimmy Anderson, who were all rested for that match.
Chris Woakes and Stuart Broad used the opportunity to press hard for inclusion in Birmingham, taking 6-17 and 4-19 respectively as the Irish were demolished for just 38 on Friday, with Olly Stone and left-armer Sam Curran completing the array of pace options.
Anderson has been recovering from a calf injury but England has indicated that he is progressing well and expects its record wicket-taker to be ready for action.