When washing machine is draining, water runs over from wall drain. I ran my auger in all the way down and only went about a foot past that point. Nothing came out, but auger was somewhat black at the end. What else can I do?

"went about a foot past that point" which point is that? The stand pipe is likely 33-36" tall and then it should be trapped before it enters the main drain. Your clog can be anywhere downstream of the standpipe, even all the way out to the city sewer where many clogs happen at the city riser. You need a much longer snake, one with a 3" cutter head. Can you see a clean out on your vent stack, try there or even from the roof if you have to.