[Kaf Hachaim, 664:60][1], tells us what to do with the lulav and esrog after Hoshanah Rabbah (the last time we use the lulav), as well as the aravos used for hosha'anas. I'm translating this from the hebrew, so I may have gotten some of the details wrong. Please correct me if I got something wrong:

 - After prayer on Hoshana Rabbah take the lulav (with hadasim and aravos still attached) home and put it over the door of the house we sleep in until Pesach, to guard it.
 - Then, in the morning before pesach, we take half the lulav and burn it with the chometz.
 - Take the other half and burn it in the Matzah baking oven.
 - Turn the esrog into jam and eat it on the night of Tu B'shvat, the new year for trees
 - give some of the esrog jam to pregnant women, to have an easy labor, and children that will grow up לחיים טובים ולשלום.
 - Take the Aravos used on Hoshanah Rabbah for Hosha'anat and put them by the head of your bed, to show how special they are to us. (this will also help protect from fear at night as [Sefer Hamidos l'Maran][2] [R' Nachman of Breslev] tells us that Klapped Hosha'anat are a Segula for removing fear). 
 - If one is really scared at night, put the Aravos under his head while he sleeps.

See [here as well][3] (scroll down to ***Halachos for Erev Shabbos Kodesh, Hoshana Rabbah***), for more sources that I didn't look up, including a Talmud Yerushalmi)


  [1]: http://hebrewbooks.org/pdfpager.aspx?req=14425&st=&pgnum=270
  [2]: http://www.hebrewbooks.org/pdfpager.aspx?req=47386&pgnum=179
  [3]: http://halachafortoday.com/ChageiTishrei.aspx