If you are looking for a way to click on a point where a spill occurs and see a line that indicates where the spill may go downstream based on topography inside or outside of a river system, the flow direction grid produced by Arc Hydro (or tools in Spatial Analyst) will provide that. There is a flow path trace tool for that. You would need to process the DEM up to the point of the flow direction grid for that function.
If you wanted to have a layer of flow paths, you could take the process further to create the steam grid or stream links (rasters) and then drainage lines (polylines).
In the DEM processing, you can "burn in" the storm drain pipes so they are like trenches in the DEM. If they are burned in correctly, they can help you trace the subsurface flow path if the oil got into the storm drain system.
GeoHMS has the same functions as Arc Hydro, but is focused on getting the data ready to export to a HMS hydrology model. Probably not what you want. GeoRAS is like GeoHMS in that it is used to get data ready to export to a hydraulic model. Also probably not what you want.