I pack low-sudsing laundry powder in a ziplock bag and wash things out nightly. I use only a little powder but I always rinse very well. For a pre-wash on stubborn stains I bring a tube of liquid detergent, but hotel shampoo works, too. A flat sink stopper is handy but I don't always bring the braided rubber clothesline, since washing on a nightly basis means there's not much to hang up. Rolling wet laundry in an extra towel speeds drying significantly. If necessary the hairdryer finishes the garment in the morning.
I just bought a travel steamer, since I love to wear linen, but I won't know if there's room in my rolly until I pack on Wednesday. Time to get new inflatable hangers, since the old ones seem to have disappeared. If you smooth the garment well when you hang it there will be remarkably few wrinkles. The shoulders of a linen blouse dried on an inflatable hanger look like they've been ironed.
I like OzBarb's ziplock washing machine!