Frequently used methods include XPS, Boehm titration, TGA and TPD. Since each of these methods has it's own advantages and also limitations, you'd better combine at least two of them together to get reliable and convincing results.
You may find it helpful to consider the methods and teachings in the following article. While I do not know the details of the synthesis of your nanotubes or purification it is often that the level of oxygen functionality is related to the defect level in the nanotubes. If you establish this then as you manipulate in further reactions you could see the change in oxygen functionality and perhaps how many sites have reacted or not.
Chemical Physics Letters 324 2000. 213–216
Surface defect site density on single walled carbon nanotubes