How can you fix rotten wood that is from the outside of the house through to the inside of the house where an old deck used to sit and caused water damage to the wall and plywood sitting on joists?

Depends how big the rotten section is. If it's small, pull out all of the rotted wood (whatever you can literally grab and pull free - it's not holding anything up anyway) and use a wood repair epoxy for rotted wood. You'll probably need to mix two compounds together and then shove it wherever you want it to replace wood. The epoxy is much stronger than wood (and much more expensive), so you can safely replace structural parts of your house with it.

However, if the rotten section is big (more than a few inches), you're probably better off tearing down the wall (exterior or interior - whichever is easier) and replacing the entire joist. Exterior will be easier if it's a small wall with siding; interior will be easier in almost all other circumstances.