We were just there in July. I was worried about this also. We had plenty of water but the faucets were still working even though they were not supposed to. People were able to get water. Bathrooms were closed and they had porta potties. Not sure if this is still true.
We towed our street legal Tracker to Oceano Dunes, no extra charge and they give you a window slip for it. If we drove it then we would have to pay extra. My brother drove his Tracker and they wanted him to pay extra so he had to load it up to bring it in. Stayed at a National Forest campground with same Tracker. Had to pay the extra vehicle fee. Coral Pink sand dunes in Utah did not require extra fee for same Tracker. We wanted to stay at Valley of Fire in Nevada but they would not let us unload our RZR at all. It all depends where you go I guess.
We took 395 form Washington to California and there are some decent dry camping campgrounds. It definately is not the fastest way across Oregon. It was good to see once which was enough. If you have time then it would be fun to explore more on the way.