Wouldn't a simple wheel odometer work just fine for this? All you're tracking is miles traveled.
No, because that's not all you're tracking. You're tracking the miles traveled *in Oregon*. Oregon can't tax anything outside Oregon, that violates the US Constitution. So they have to prove to a reasonable standard that all the mileage they're taxing was driven in Oregon.
To add, for those who haven't looked at a map, the Portland metropolitan area, which is where the bulk of population in Oregon lives, is right on the border with Washington state. A large number of people commute and and regularly travel between Oregon and Washington. Any state level taxing solution needs to account for this.