Annie's wand is made up of Elder Wood and Horned Serpent core. 

About the wand: Elder wood is the rarest wand wood to date, and many people who crosses its path consider it as 'unlucky'. It contains highly powerful magic that not very many witches or wizards are able to control/master. You have to be a highly respected witch/wizard to possess this wand. Those who own an Elder Wood wand are highly unusual witches/wizards, and are marked out for great destiny. They are loyal to their masters. 

Horned Serpent core: Horned Serpent cores are very powerful. They were sensitive to Parseltongue, and would vibrate when 'spoken to'. They could also warn their owners of danger by emitting a low, humming sound. 

Dante's wand is made up of Ebony wood and Hippogriff feather.

Ebony wood is an all-black wood (see picture above), and it's well-suited for combative magic & Transfiguration. It is said that they're good matches for those who are courageous, non-conformists, or comfortable with being an outsider, and are willing to stand by their beliefs. They have special skills such as: purifying, protective, healing, communication, and love magic. 

Hippogriff feathers: They serve those who are noble, respectful, protective, short-tempered, stable, fiery, adaptable, versatile, graceful, and courageous. Having a Hippogriff feather in your wand suggests that you can adapt in any situation, no matter how impossible things might seem. Like the creature the wand core comes from, the owner demands respect. The wand core works great in Transfiguration, Care for Magical Creatures, Apparition, Divination, and Dueling hexes, as well as healing and Hexes.