I STRONGLY SUGGEST THAT YOU MAKE A BACKUP OF THE MESH YOU ARE TRYING TO FIX IF YOU DO SOMETHING WRONG!!!
First of all you need NifSkope...you can get it here:
NifSkope Download Page
Install it and let's move on with this.
Locate the mesh that has the wrong texturing path. The path for meshes is :Data\Meshes (before Data it's your Oblivion install path). For example at me : D:\Maafiaman\Games\Elder Scrolls IV Oblivion\Data\Meshes.
For this tutorial I will treat one of my retexturing mods (a sword) as a wrong texturing path. Also some modders don't use the default folders (example: Armor meshes in armor folder...for info check the mod archive (.rar, .zip))
So for my sword I will go to: D:\Maafiaman\Games\Elder Scrolls IV Oblivion\Data\Meshes\Weapons\Sword of the Gods. In here I see a nif file named longsword.
I open it with double click (if NifSkope hasn't activated the afiliations with the nif file types, double click on the file, click on Choose Program and browse to the NifSkope installation folder, select NifSkope.exe). Default NifSkope installation folder is : C:\Program Files\NifTools\NifSkope
Here you can see where you can find the texturing path


You can see here that the sword is totally white (in Oblivion it shows a purple texture) and that the "NiSourceTexture" path is set to C:\Program Files\Bethesda Softworks\Oblivion\Data\Textures\Weapons\Sword of the gods\sword2.dds and the other one is he same only that it's marble.dds, but my game has a totally diferent installation path and besides the meshe shouldn't contain the whole installation path.
So what are we gonna do is is double click on both the "NiSourceTexture" (must be set one at a time) and type
(without the quotes) "textures\weapons\sword of the gods\sword2.dds",hit enter and for second "textures\weapons\sword of the gods\marble.dds" then hit enter again.

You can see that I have set the texture path to "textures\weapons\sword of the gods\sword2.dds" and now the sword has the texture
It is kind of late and I am tired so I don't know if I explained it too well