Watering plants with soaked forest soil
You are thinking about something like "compost tea".
http://www.homecompostingmadeeasy.com/composttea.html

The problem is that a random piece of forest soil may or may not be rich in nutrients.  If that soil has water soluble nutrients in it, wouldn't the rain have already rinsed them out?

If you make tea out of compost, there has been no chance for rain to rinse out nutrients because the decomposed stuff has been in your compost bin.  

Last piece: if you are making tea out of forest soil or compost, when you are done you will have a soaked clump of wet soil or compost.  What are you going to do with it?  Probably throw it on the ground somewhere.  It might make more sense and be much less messy to skip the tea step, put the forest soil or compost on the ground next to your plants, and then water them.