Character Analysis
Theodora came to Hill House to study the paranormal because she had a fight with her roomie, and needed a place to crash while things cooled between them. Perhaps that bears repeating: Theodora is the type of person who would live inside a haunted house simply because she needed a place to sleep. If that doesn't say volumes about a character then we don't know what does. She quickly becomes chums with Eleanor, and their relationship provides the emotional center for the horrific conflicts at Hill House
Live Like We're Dying
Theodora's a real go-getter—just the opposite of our repressed heroine Eleanor. When she first arrives at Hill House, Theodora dresses in the color yellow, and Eleanor points out she "bring[s] more light into [the] room than the window" (2.73). Theodora's hunger for life appears every morning as a ravishing hunger for breakfast. And when she's not doing something, she sits by the fire, soaking in the heat like a cat and pining for something to do.
It's easy to see what attracts Eleanor to Theodora, as Theodora is everything Eleanor is not. Eleanor is reserved and self-conscious, while Theodora is outgoing. Eleanor requires the acceptance of others for validation, while Theodora does the validating with no one's help. Eleanor is inwardly focused, while Theodora—well, you get the idea.
Perhaps this quote sums up the relationship between the two women best:
[…] looking at Theodora, it was not possible for Eleanor to believe that she ever dressed or washed or moved or ate or slept or talked without enjoying every minute of what she was doing; perhaps Theodora never cared at all what other people thought of her. (4.14)
For Eleanor, Theodora is a mirror, but it's a mirror that presents all of her flaws for her to see.
The Nameless One
Maybe you've noticed that Theodora doesn't have a last name? That's not a fluke on Jackson's part. That lack of last name is an important clue to her character.
Eleanor, Luke, and Dr. Montague—especially Dr. Montague—are all given last names. At the same time, all these characters are in some way controlled by their families. Eleanor needs to steal a car to bypass her family's restrictive rules, Luke is only at Hill House because his aunt demanded he come, and Dr. Montague, well, have you see how his wife treats him?
Theodora, on the other hand, is free of the family and all obligations to it. We never hear about her relations. We know she has a roommate somewhere, but they aren't on speaking terms. Theodora's free spirit is shown by the fact that her individual name only is given to the reader. Unlike the others, she's not tied down by a family or a home.
Theodora's distaste for family life is perfectly displayed by the haunt she and Eleanor witness in the forest. They see a ghostly family having a picnic by the brook: mother, father, children, puppy, the works. Theodora screams for Eleanor to run and not look back. When they return to Hill House, Theodora "laugh[s] in a little continuing cry, laughing on and on thinly" and admits that she looked back (6.81).
What Theodora sees when she looks back is never revealed to the reader. That's certainly a bummer for our analysis, but we can still dredge some important notes from the whole scene. Unlike most haunts, this one seems to be directed at terrifying Theodora only. Eleanor is rightly scared at the sight of the ghostly family (they are ghosts, after all), but it's only when Theodora panics that Eleanor runs, too. Also, while we don't know exactly what it was Theodora saw, we're willing to bet it had a lot more to do with the family than with that puppy.
Family and obligation: they scare Theodora like a plague. No, like the plague.
Homewrecker
Theodora's revulsion to all things family makes her a natural homewrecker. No, not homewrecker as in someone who goes around breaking up marriages; we mean a literal homewrecker.
We occasionally see Theodora discussing a need to destroy houses and house-like objects. She offhandedly mentions arriving at Hill House and says how much "fun it would be to stand out there and watch [the place] burn down" (2.57). She also recalls an incident in her childhood when she threw a brick through a greenhouse and loved the sound the crash made (3.106).
Unlike Eleanor, Theodora doesn't require a home or family to be happy. She's perfectly capable of being a one-woman show. When Eleanor asks to move in with her, Theodora responds: "I am not in the habit of taking home stray cats" (8.26). This incident further cements Theodora's need to avoid all things homey, and it is what ultimately causes a rift between her and Eleanor. Theodora grows colder to Eleanor after this because she feels Eleanor is trying to tie her down. And Eleanor, unable to find a home with Theodora, is driven further into the halls of Hill House.