I agree with the above. It's really about what you want and what you think will make you happy in the long run.
If you want to apply to Harvard and Princeton, to give yourself those US options, then take the GRE.
Have you taken any of the practice tests yet? If not, download Powerprep and take one. It's only a few hours and you can get some idea of how well you'll do on it (without the extra studying). You can judge then whether you think it'll be worth your time or not.
In the end it could be better to have applications at the three and see what happens when offers are made and make your decision then than it is just to have an application at Oxford and not have the choice.