I have created a 3d model in sketchup and exported it as an obj file. However, when I drag it into the filming area, all the textures are gone and it's nothing but grey and white. I would obviously prefer that all my textures and colors remain as they are in the obj file.

Adding a closeup of the object menu to show textures...
You can import the textures through the object's inspector.
If I understand you correctly, I have to choose each of these items and import the textures one by one?