How does Janie struggle to free herself from the power of Nanny, Joe, and Logan, and how does the author use this power struggle to enhance the meaning of the work?

Janie spends the grand majority of Zora Neale Hurston's Their Eyes Were Watching God attempting to find her own horizon.  She grows up under the hand of Nanny, a former slave who looks for little more in life than peace and security.  Because of Nanny's outlook, she guides Janie into what basically amounts to an arranged marriage with a man named Logan Killicks, an older farmer who, although rough around the edges, owns land and can provide for Janie.  However, the marriage is loveless. When Janie shares this information with Nanny and complains of her unhappiness, it upsets Nanny greatly.

Nanny sent Janie along with a stern mien, but she dwindled all the rest of the day as she worked. And when she gained the privacy of her own little shack she stayed on her knees so long she forgot she was there herself.  Towards morning she muttered, "Lawd, you know mah heart. Ah done de best Ah could do. De rest is left to you." She scuffled up from her knees and fell heavily across the bed. A month later she was dead.

Janie thought that love would eventually develop, but it never develops.  The relationship begins to devolve further when Logan begins to insist that Janie do more and more of the chores around the house.  Janie takes a stand, insulting Logan for both the way he treats her and for his appearance.  He gets very upset with Janie, and their relationship deteriorates.  Eventually, a man named Jody Starks comes walking down the road in front of the house, and Janie makes a point to try to get his attention.  They talk and hit it off, and Janie begins to see in Jody an opportunity to change her life.  At first, Janie's feelings are ambivalent: "Janie pulled back a long time because he [Jody] did not represent sun-up and pollen and blooming trees, but he spoke for far horizon. He spoke for change and chance."  This change is something Janie wants, and she eventually runs off with Jody to a town called Eatonville.
In Eatonville, Jody begins to establish himself.  He becomes mayor (after running uncontested), opens a store, and begins to buy Janie fancy things.  He wants her to look good. However he does this not so that she will feel good, but so people will see her and think more of him for the way he treats her.  Eventually his treatment of her devolves, as he wants her to been seen, but he does not want her to speak.  He then begins to berate her, and she loses hope of the opportunity that she thought would be part of her life with him.  He then begins to criticize her looks around the store, in front of other people, until one day when Janie retaliates, telling him, "When you pull down yo' britches, you look lak de change uh life."  This marks the breaking point in their relationship.  After being publicly humiliated in this way, Jody's health grows worse and worse, and he soon dies.  
After Jody's death, Janie continues to run the store, but she still feels unfulfilled until she meets a man named Tea Cake.  In Tea Cake, she finds the connection she has been looking for.  He treats her well and respects her, and even though they have some bumps in their relationship, she understands him. He helps her grow less callous and more compassionate.  She finds herself wanting to do things she avoided in the past.  While she detested the physical work that Logan expected of her, she willingly moves to the Florida Everglades and works alongside Tea Cake on "the muck."  Even though he cannot provide for her as Jody did, she is happy to be poor with him.  Although their relationship ends in an unfortunate tragedy, Janie is able to find her own horizon:

Here was peace. She pulled in her horizon like a great fish-net. Pulled it from around the waist of the world and draped it over her shoulder. So much of life in its meshes! She called in her soul to come and see.

Despite the toxic nature of most of her relationships, Janie was able to take something from each of them to help her become a capable and content woman.  Without her various struggles for power, Janie never would have discovered her own identity or learned that true power emerges through compromise.