I have just today driven from Van to Erzurum along the following route:
Van heading along the lake towards Dogubayazit on the E99/975, turning on the 280 towards Ercis at the top of the lake. From Ercis the 280 heads to Patnos and then turns north to Agri. The roads are all very good, many stretches with new tarmac and only a few areas of gravelly surface. Some contraflows through roadworks but only for a few km at a time. The scenery is impressive too, lots of river gorges and wide agricultural valleys. From Agri I headed west towards Horasan and then onto Erzurum. The whole trip took me 6 hours including stops for tea, lunch and photos. There were some police vehicles parked by the side of the road, but no roadblocks or evidence of any disturbances, and warm friendly interactions with local people as per usual. The road was busy with trucks and wedding parties and people going out fishing, picnicking etc. And the usual precautions re keeping an eye out for vehicles veering off the road or towards you etc need to be taken.
I took this route as I decided to avoid Diyarbakir as the Foreign office is advising against all but essential travel and there has been a lot of footage of the riots going on in Diyarbakir over the last few days.