I would like to add a few new objects to my mod using original Oblivion nif files, but with new textures. My question is, if I would make these altered nif files available for download, would I be breaking any copyright rules?

It would be breaking copyright rules, however anyone with Oblivion should already have those nif files so you shouldn't need to include them.

No, what you are doing it 'retexturing' and because having the game is required to use the mod. This is what all mods have to do since the CS does not have 'texture sets' available. (a new feature that is in the FO3 GECK)

Well, I need to change the texture path of the nif file to the new texture, so have to include the nif surely? I know many mods do this (like Elsweyr, the Deserts of Anequina).

Ah, I thought you were asking to include unaltered content in addition to the altered content - I thought that was an odd request.

You're fine

Great, thanks!