The quickest and easiest way is with a moulding nailed up to cover the corner entirely. Use a 1/4 round or cove or crown moulding. At home depot you can buy decent "finger jointed" paint grade, pre-primed mouldings pretty cheap. Just put them on saw horses and brush on a finish coat, then measure, cut and nail up. Done. Or, if the cracks are small then you can try calking them with vinyl calking. If the repairs are more involved I would go with mouldings vs. drywall repair b/c drywall repair to an inside corner with popcorn ceiling would mean that you could never match the texture that you would have to remove from the edge of the ceiling and also you would have dust everywhere and you would probably have to prime and paint and also paint the whole wall and ceiling to match the repair. Mouldin is sounding pretty good right now huh?