My version:

Reference images:

Analysis (whoo, scientific): Yes, these are three different styles, but they're all somewhat similar. Troi's style is her basic Season 1 hairstyle, only instead of all the hair being coiled into the bun, some of it hangs from the middle of the bun. Picture 3 is from (obviously) the original series, in which a guest star had a hair-wrapped ponytail. Picture 4 from "For the World Is Hollow and I Have Touched the Sky" features a similar style, with the ponytail coming from the center of a bun.

Directions: I just did a normal wrapped ponytail, as in picure 3. This is pretty easy; put your hair in a high ponytail, take a small piece of hair, and wrap it around the elastic holding the ponytail, pinning it to hold. The picture 4 style is a little harder. Make a very high ponytail, and wrap 2/3 of the hair in the ponytail around the remaining third, forming a bun. Pin to hold, and that's it. Troi's style is quite a bit harder. See the Season 1 page for details on how to make the tall bun. When you get to the step where you wrap the hair around the "tower of elastics", leave a portion of the hair to fall from the bun while you wrap the rest of it. You may also want to leave out hair at the beginning for more braids, as you can see in picture 2 that there are a lot of them wrapped around the bun. That's it!