Add a damp-proof membrane.

Oh boy, there,s only about a hundred things that could lead to that kind of problem. I would start with venting; kitchen and bathroom fans, attic vents, etc.. If your house is super tight, (insulation and vapor barrier) a permanent 4 inch open vent in the kitchen should be provided. Check your roof integrity, foundation drains, and anything else you can think of. You may need a specialist.

Are we supposed to guess where you are located or what type of wall structure you have?

Is it particle board or concrete?

Install an air to air exchanger.

If water enters the wall at the foundation ;I use a long concrete drill and drill holes from the inside of the wall at about 45 degrees downwards every 500mm, fix a thunnel with plastic pipe attached, to a hole and pour as much as possible "sillicon water repellant" in.

On the outside you can first wire brush the loose stuf, then spray or paint with the same stuf. It will displace the water and form a water tight gell that can not be seen.

Insufficient data to give more than a general reply. I have seen this problem in poorly built homes here in Canada, and the paint is not the problem...the problem is moisture in the wall.

Water is getting to where is should not be. Stop it from getting in, channel it away, create vapor barriers. If you were in Canada, I would say your problem was "no vapor barrier" since the vast majority of houses in Canada are constructed with wood, with fiberglass insulation. Moisture condenses at the temperature gradient between hot and cold, usually inside the insulation. Sometimes the vapor barrier is installed incorrectly...on the cold (outside) side of the wall in a misguided attempt to stop breezes. In some climates, it is always hot outside, and the "cold" side of the wall is the inside, the air conditioned side. Again, you get moisture condensing out where it should not be.

Remove the interior drywall, rip out the sodden insulation, put in fresh dry insulation, install a new vapor barrier and nail up new drywall. That IS the quick fix. If you do not do this, the wall will rot and fall down.