Shells can give a temporary water resistance boost, or can be sold.
The painting is not a quest item.
Soap is used in one of the ways to craft lockpicks (with a key). In a pinch you can use a guitar or pitchfork as a weapon; generally you can just sell them.
You can put a chest or other container somewhere to stash stuff. Eventually a dedicated storage area will be opened in the End of Time.
