They can be repaired with any other variant of the robe; this includes the hood, i.e. the hood can be repaired with the robes and the robes can be patched up with the hood.
Oasis villager robe
Worn by most Treeminders, this attire has less body coverage than the Oasis robe. As a result, it is slightly lighter but also worth less.
One can be found on a dead branchtender in the underground Oasis caverns, just down the path from the entrance.
Oasis druid hood
Aside from Treeminders, this hood can also be found on Drifter at Dickerson Tabernacle Chapel. Poplar's hood, a special version, is given to the Lone Wanderer as one of the possible rewards of the Oasis quest. However, if the Lone Wanderer's hair is tall, it will show out the top of the hood.
Oasis exile hood
|The following is based on Fallout 3 cut content.|
Another version of the druid hood called "Oasis exile hood" can be found in the game files but is not used in the game. It is identical in looks and stats with the regular hood except for increased item value. It can only be obtained via console commands.
|End of information based on Fallout 3 cut content|
If you drop the druid hood and move it, then the game will still have the hood where you dropped it. It won't be visible and you can walk on top of it, but the crosshair will say "Oasis Druid Hood" and when you pick it up it disappears from the place you moved it to. [verified]