You'll need a BSA unpacking program like
BSA Commander to get the default texture,
DDS Converter (or a DDS plugin for Paint Shop Pro), a program like OBMM for archive invalidation, (If that's the program you're going to be using to retexture)
First, use your BSA program of choice to find the Arena poster textures (To save you some work, the filepath is Textures/Architecture/ImperialCity/ICArenaPoster01.dds) and extract them somewhere you can work on them. I don't know how Archive Invalidation works, but you might also want to extract ICArenaPoster01_n.dds.
If you got DDS Coverter, convert ICArenaPoster01.dds into a format Paint Shop Pro can use and open that. If you got a DDS plugin for it instead, just open ICArenaPoster01.dds in Paint Shop Pro. Looking at the texture, since it's mostly a single 2D plane, it should be pretty clear how any changes you make will affect the poster in-game. Change it however you want.
Save it as a DDS if you got a plugin, or turn your new texture into a DDS if you got DDS Converter. I know next to nothing about editing Normal Maps, so I can't help you if you want to change how light reflects off it...
Paste the normal map and the new .dds file in in Oblivion/Data/Textures/Architecture/ImperialCity, making new folders if necessary.
Open up OBMM, click Utilities, then Archive Invalidation, check "Textures" under File Types to Include, and click Update Now.
That should do it.