Mags
Could Martha be her middle name - I have loadsof instances where say Mary Ann is known as Ann/Annie so she could have been called by another first name with Martha as her second name.
Also, try to see if you can find her in 1891 - if you want sonmeone to look for you in 1891 you will need to post all occupants at her address in 1881. She may have a different name/age/birthplace in 1891! Also, are you sure she was 4 in 1881, it could be 4 days/weeks/months and transcribed wrong....
Hope you find her!
Claudia
PS There is a Martha Johnson Sep 1876 Oldham 8d/711 who would have been 4 in 1881 - Oldham/Rochdale VERY close!