Exterior paint doesn't care which side of the wall it's on. It shouldn't stink.
Stink is usually caused by old paint that has gone rancid because of mold or fungus growth, because modern paint isn't toxic enough to suppress mold growth. You don't save any money using old paint. And unfortunately when they crack the can to mix a custom color, that breaks the seal.
Unfortunately, in the experience of most people that this cannot be "sealed up" - many have tried using sealers or bleach treatments, never works. After they've tried sealers and found they didn't work, the job of removing the paint is much harder.
The only option is to entirely remove it - fortunately fresh latex paint is fairly fragile. Blast a humidifier in that room continuously so it doesn't harden any further, and then tear it off the walls by wetting it and going to town with harsh scrub brushes, paint stripper, whatever it takes. Lots of physical labor, but sorry, no one is able to seal it.