As for the robes themselves... Night Goblins have become so accustomed to living in dark caves that they have become a distinct sub-species. The robes shade and protect them from the bright sunlight when the Night Goblins are out in the open. Thre dark colouring probably has to do with endless dirt and grime - it's not like they wash, and each set of robes has probably had many, many, many owners before... each of which probably met a bloody end. Where the robes come from is pretty much left to the imagination, and probably boils down to "wherever they can get them". Nightly raids on the surface world. Silk spun from repulsive underground worms or spiders. Stolen from slain Skaven (or perhaps even made from the skins of Skaven or Squigs).
Night Goblins get from place to place the same way Skaven do. Between the natural cave systems, the innumerable lost or abandoned Dwarf mines and tunnels, the lairs dug out by monsterous underground creatures, and the great fractures ripped beneath the world by the Skaven, there is probably endless potential for getting from place to place underground (for anyone suicidal enough to brave the dangers). Night Goblins will happily venture across the surface in the dark of night, and begrudgingly during the light of day under the cover of their heavy robes (no doubt this happens often during a Waaagh).