I don't know if you received info about this yet, but here is what I found. Unfortunately, it doesn't look like any of them is your James H. Jordan.
In Moscow, Latah Co., ID in 1920 (ED 121, p. 2B/217), I find only one Jordan, an Ola Jordan, female, B,age 27, wd, born MS. There are two children listed with her: Stanley A., son, male, B, age 5, s, born Moscow; William A., son, male, B, age 3, born Moscow. These three are enumerated with a John W. Settle family and Ola Jordan's relationship to the head of household is listed as daughter.
Also in Latah Co., although not Moscow, is the following: ED 116 Four Mile Precinct p. 3A/155 6363Jordan, George A.headO F MW54MIowaKYVTfarmergeneral farm Jordan, PhoebewifeFW53MIowaPAPA Jordan, William N. sonMW15SOre.IowaIowa
ED 116 Four Mile Precinct p. 3B/155 6565Jordan, James F.headO MMW24 MOregonIAIAfarm laborerpoultry Jordan, Florence M. wifeFW21 MSDWisc Wisc Jordan, Dallas F.sonMW1 10/12IDOreSD
Lastly, I found a James H. Jordan in Idaho Falls, Bonneville Co., ID (that's mighty far from Moscow) ED 104Idaho Falls City, Prec. 4 p. 5A/103 94 100Jordan, James H. headO FMW56MUTEnglandScotlandoccupation none Jordan, AnniewifeFW46MUTSwedenSweden Feraday, JanesisterFW50MCAEnglandScotland