Hopefully someone can chime in with more insight than me, but here is my limited experience.
Vulcanite= Black hardened rubber. Can oxidize over time.
Lucite= Not sure exactly what this material is but I have heard others call it "acrylic". Can be black and shiny just like Vulcanite, but can also come in a variety of other colors and patterns such as blue, purple, red, white, etc.
Cumberland= Again, not exactly sure what this material is, but it usually looks sort of auburn/red/mahogany in color, most popularly used by Dunhill as far as I know.
Again, I hope someone can chime in with more experience than me, this is just solely what I know on the topic.