I swear by the expensive synthetic socks I bought for walking all day. They wash easily and seem to dry in a minute. Same with a microfiber towel.
Tide makes great little one use packets of detergent, better than Woolite. For drying go to the camping section and look for a nylon line. It has two or three stretchy strands woven together that you can hook a corner of the fabric through and hang anywhere.
I, also have an upcoming trip to Europe. I travel with three days’ worth of clothing, and do my washing every night (it takes more than overnight for things to dry). I use regular powdered detergent, and it gets things clean enough.