The HBO Soundtrack has songs written for the show by contemporary artists.


However, here is the list for the original releases of those songs, from the 1920's.
From Archives.org, free to download

Enjoy :)

01_Livery Stable Blues_Original Dixieland Jass Band_1917
http://goo.gl/3W2xR

02_The Dumber They Come_Eddie Cantor_1923
http://goo.gl/szPBD

03_My Man_Fanny Brice_1928
http://goo.gl/NVysf

04_Darktown Strutters Ball_Jungle
http://goo.gl/ULDhY

05_Crazy Blues_Mary Stafford
http://goo.gl/T7UXQ

06_Mournin Blues_Original Dixieland Jazz Band_1918
http://goo.gl/lG9U7

07_Some of This Days_Sophie Tucker_1926
http://goo.gl/E0ShD

08_ Margie_Frank Crumit_1920
http://goo.gl/Yq1lk

09_Carrickfergus
Hmm.. not really from the 20's

10_Wild Romantic Blues_Jane Green
http://goo.gl/F9ppQ

11_After You Get What You Want, You Dont Want It_Van & Schenck_1920
http://goo.gl/n5t7a (Youtube)

12_The Sheik of Araby_The Palm Court Theatre Orchestra
http://goo.gl/4ydgm

13_Japanese Sandman_Olive Kline_1921
http://goo.gl/9Q0Hg

14_Don't Put a Tax On the Beautiful Girls_Eddie Cantor
http://goo.gl/iQb0e (iTunes..sorry)

15_All by Myself_Aileen Stanley
http://goo.gl/xwNmS

16_Life Is A Funny Proposition After All_George M Cohan_1911
http://goo.gl/2KBUl

17_Maple Leaf Rag_Bonus Track_United States Marine Band_1906
http://goo.gl/DCy2s

18_Alice Blue Gown_Bonus Track_Edith Day_1920
http://goo.gl/uqpq9