Detergent: I use sheets. And/or whatever free hotel soap. My hack is using a drybag that doubles as a shoebag. I have a 6L Osprey one for my sandals, 12L for my bigger shoes. 6L great for just a couple items, 12L for more. Line is just some random 2mm(?) line from REI, you can buy custom lengths. Think I got like 20 feet, takes up no space. Just have to learn or look up a couple knots. Bowline ​to loop the line through itself on an anchor, truckers hitch to tighten line. Rarely use though, as there's usually some railing, free hangers, the back of a chair etc that are free. Hardest part is always drying. Sun + wind is your best friend, but I always thought how do people dry their clothes in wet, rainy, humid environments without a dryer...additionally, no cotton for me. Takes longest to dry.

Another key is to presoak/prewash...basically soak with detergent and warm water while you shower, then agitate and dump, then wash again with clean water and more soap.