Really, you should be asking these questions of a qualified tax accountant.
I do not know anything about Oregon tax laws, but if you are saying they do not have a sales tax, then my understanding is that you would not need to charge tax. But then again, I am not a qualified tax accountant, and it would not be wise to make business decisions like this on unqualified advice.
The only articles I could point you to for further clarification would be the Oregon State Tax code.