This seems very complicated. I think the confusion is partly because of the habit in the 18oos of giving an address as xxx st, yyy road, where XXX st runs off YYY road. Going from the maps and directories it looks as if, before 1892 there were no houses listed in Oldfield rd and no road of that name is seen in Kellys. there is however in the index of roads (which often includes small roads and terraces which are not listed as having houses in the main street index) an "Oldfield road, Ombersley road" , which means it ran off Ombersly road, which was parallel to Henry St. Henry St was a pretty new road at that time.
In the 1892 edition Henry St is again listed . There is also mention (see below) of an "Oldfield St, now called Kingsley road", which runs at right angles to Ombersley road and what is now Oldfield Rd.
In the 1895 Kellys there is no Henry St (in Balsall Heath, though there is another off Great Lister St), but Oldfield Rd is included. So it looks to me as though Oldfield road (or st), which had only a very short existence, changed its name around 1891 to Kingsley road, and shortly after Henry St was changed to Oldfield Road. The reason for the last change would almost certainly have been to reduce confusion with the other Henry St.The Kellys entries for Henry st (1892 ) and Oldfield Road (1895) seem to show that no renumbering took place, though the number of houses increased considerably. Note Kellys date is publication date and should be taken probably as the year before
The Kellys entry for Henry st 1892, the entry for Oldfield road for 1895 , and the entry for Oldfield st for 1892 are shown below, as is a map c1905 showing the relevant area