England's first match of the competition, and their first under interim coach Stuart Lancaster, comes against Scotland at Murrayfield on Saturday.
Gloucester pair Narraway and Trinder were due to be part of the senior squad ahead of that match but will remain at their club for treatment on respective calf and ankle problems.
Narraway's absence opens up a space for Leicester's Waldrom to come in as a number eight, while Bath's Banahan comes in to cover at centre and wing in place of Trinder.
Both incoming players played for England Saxons in their 23-17 win over the Irish Wolfhounds at Exeter on Saturday.
Lancaster is already preparing with for the Calcutta Cup clash without Toby Flood, Courtney Lawes (both knee), Manu Tuilagi (calf) and Tom Wood (foot).