Edgar and his wife, Marian McClure Wood, lived in Cleveland Heights, OH, and were members of the St. Paul's East Cleveland Episcopal Church (shown above as it looks to Google Maps street view, these days). This is where they went to Ash Wednesday service when they met cousins Edith and Dorothy.
I can't find any other references to Wise or Nicholas in family records, although my sis-in-law remembers a "cousin Edith" attending her wedding (1970s) in Cleveland.
Of course, I haven't finished reading his diaries...so maybe Edith and Dorothy will show up again in an entry later.**
**24 hours later, I'm still reading diaries and have found more entries about Edith & Janice Wise indicating they were Edgar Wood's cousins, living somewhere not far from him in Cleveland area. Dorothy Nicholas is in town one day in 1968 for her granddaughter's wedding, and that prompts Edgar & his wife Marian to visit with Edith & Janice Wise and Dorothy, who's there. Now to track down exactly which branch of the family the Wises are from...
2022 update: Dorothy and Edith were Edgar's 1st cousins. They were the daughters of his aunt Adelaide Mary Ann Slatter and her husband, James Sills Baker. I connected with folks from those families last year!