Thanks for the additional photos, really shows the beauty of your pearls! The clasp seems to be missing the fish hook insert. The nacre appears to be very thick, and from the photos, the pearls seem to be in good condition, but would need to be examined closely to check for cracking around the drill holes and in the nacre.
As Pearl Dreams suggested, they do need to be restrung and a nice clasp added. Round pearls with excellent luster do generally command a higher price than baroque, but many pearl lovers prefer organic shapes.
A true family treasure and conversation piece!
To get a very rough value for your pearls, do a search on ebay for "vintage akoya pearl necklace." You may find a similar strand.