Washing them is easy! You can do it yourself.
Swish a bit of mild soap in some water. I prefer to use distilled water to avoid both chlorine and possible hard water minerals, which combine with soap to make a hard to remove scum. (I speak from experience. Our well water is hard.)
Then soak the pearls in the solution for 15 minutes or so, and then remove grime with a soft cloth, cotton swabs, or a soft brush.
Rinse in more distilled water and then lay them on a towel to dry for 24 hours or so. (The silk inside the drill hole takes a while to dry.)
At that point you can restring them, if you like.
Now-- their value.
Value can be sentimental value (which no one can put a price on), replacement value, or resale value.
An appraisal would tell you replacement value (for insurance purposes), but these pearls are not so very valuable, and I don't think they need to be insured.
If you wish to sell them, then you are really talking about resale value, which is lower than replacement value. Unfortunately pearls do not tend to retain value on resale. But you can get an idea of what you might get for them by searching on eBay for SOLD necklaces like yours.