I generally take three each of the major items that are likely to get smelly and dirty. That is, three pairs of bike shorts (although only one or two pairs of overshorts), three pairs of woollen socks, three shirts or jerseys and three pairs of gloves.
It pans out that one set will be one on me, one in the dirty clothes bag, and one set spare. The additional clothing set is not a significant space or weight problems, and I toured fully self supported in Europe in 2003 and 2007 with just two rear panniers, a bar bag and a tent.
I've had too many occasions back when I started touring swhen I tried getting into damp-to-wet clothing that I washed the night before and hung out to dry (eg, washing in restrooms, showers and the like). With some luck and judicious use of wet wipes, I can get almost a week of cycling out of the three sets without offending anyone, and likely end up at a campground, hostel or other accommodation where laundry facilities are available.
Laudromats are also excellent for being warm and dry refuges when the weather turns nasty. If you have hygiene issues, then get a bottle of household first-aid disinfectant (such as Dettol in Australia which comes in very small bottles), andput a dose of that into your wash cycle. I've never done this in extensive use of laundromats, and I haven't contracted some nasty disease.
And if you are a swimmer, there is nothing to stop you from using various rivers and lakes to take a dip clothed. It probably won't do that much to wash away ingrained dirt, but can help.
And if you are concerned about synthetics retaining nasty smells, see if you can buy some borax powder for every third or fourth wash (wherever that might be). It kills the organisms that end up in the fibres of synthetic clothing and generate thoae unwelcome odours.
Bekologist also is right about the sink plug. Mine is a piece of thin, flat moulded round white rubber about six inches in diameter that actually lives in my Trangia cook kit. It is designed to fit plug holes of many different sizes (so carrying just one plug won't work on every sink) and has served me very well.