Disable the gamepad and or rumble. You may have to do this in both the INI's and Prefs files. And, do this in both the root install and in My Documents/My Games. Note, make a back up of the files in the root directory, hose those and you have to reinstall the game.
Search all the files for "gamepad" "controller" and "rumble" and set the values so they are disabled. Note, usually this is setting them 0, but one requires a 1 (it is something like disablegamepadtrue=0, needs to be a 1)
I do not recall seeing options for that in Oblivion, unless it is in a different version. Also, for me, I only have one INI file.
OP, whatyour specs? Mods installed? Do you use BOSS?
It's called the Joystick specifically in Oblivion. Oblivion will auto detect any controller you plug in and then try to make that the controller the default. This can cause the stuttering and lag when there are no other apparent reasons.
Oh, I see I thought it was like Skyrim where it had the option automatically in the menu.