There are reputedly relics of a Roman encampment at Metchley Fort, between Selly Oak and Harborne, and Rykneld Street is supposed to have been a north-south Roman road which was followed by parts of Pershore Road in Stirchley, Icknield Street between Spring Hill and Hockley, Wellhead Lane in Perry Barr, and bits of Kingstanding. When I went to school 6o years ago we were told that you could still see the camber of the old Roman Road in Sutton Park, not far from the Parson & Clerk pub, but I never found it, although I was always on the lookout for things like that.
You can read all about this sort of thing on the superb free website of the Victoria County Histories, Volume 7 (Warwickshire) - Mr Google or others will find it for you, I'm sure.
Peter