How to clean old acrylic costume jewelry? - lucite beads

Oh, how I scored at an antique store!

Acrylic age ( "Bakelite?) Suspension of the chains and bracelets, earrings, fashion bracelets and a ton of plastic.

So much so that very beautiful and I love to do things outside, but it is dirty, with sticky powder, a film about him.

Someone knows how I can clean the film without damage to the accounts that appear to be painted with acrylic?

They are so beautiful and light, perfect for bracelets and earrings, thick, but I'm afraid I will destroy them: (

Any tips?