I have pop up mesh hampers in all the bedrooms. They have handles so it's easy to carry them to my laundry closet. I didn't get huge ones cause it keeps the amount of laundry that will fit low and light!

So, I wash them more often and don't get behind.
As far as wet things like towels, I have a 3 bar rack that hangs on the back of the bathroom door to hang them to dry. Once they are dry then they go into a divided laundry hamper that is in the laundry closet.
Wet clothing I do the same way til they dry then they go in the person's hamper they belong in. (I don't keep a hamper in the bathroom cause it's just asking for wet clothes to sit and get funk in it! Yuck!)
Now, on things that are messy like poopy leaks, spit ups, food spills, something that really stains, etc. I rinse them and let them soak in the sink for a bit. Then I'll gather the appropriate colored items in all the bedrooms and wash them immediately. If I have to, I just chunk them alone in the washer and let them soak then wash. But, those things never make it in a hamper...and they are never allowed the chance to dry.