I have been trying to overlay two shapefiles of the Harare Zimbabwe streetmap one with centerlines and the other digitized as polygons. the challenge i am facing is that the two overlay but not on the same position they are both projected to wgs 1984 utm zone 36s.
Such a slight systematic shift is usually due to a lack of datum transformation before reprojecting the data. You should test the different transformation and your data will overlap correctly. I can't tell which one is best for you based on the information provided, but you can test it relatively fast.
EDIT: if this doesn't work, you have two solutions: The rigourous is to try to find the real CRS as the wrong CRS could have been assigned. Therefore you need to remove prj file of the suspect shapefile (rename with "_old.prj", do not delete) and test all possible CRS by changing the dataframe coordinate system.The pragmatic solution is to use the spatial adjustment tool (in an edit session, make a copy of your shapefile first) in order to adjust the suspect shapefile with links on the reference one. Start with affine transform, and if you notice more distortion you can use rubber sheeting (but then you need far more links, rubber sheeting is really the "last chance" option). Note that your polygon and lines don't seem to have the same precision, so you should not expect a perfect result.