Sorry, but I can't help Karina. There is a lot of Klezmer music on the Web. I went to one site only and found the following tunes. Perhaps along the way we may find a treasury of lots of Klezmer lyrics.

16 Turned The Boy

Ahavatia i

Alef

Baklava - the Middle Eastern treat

Baruhk's Boots

BaShana HaBa-ah

Borhki Nahfshee

Daled

Dayagim

Eli, Eli

Eretz Tropit Yafa

Erev Shel Shoshanim

Frailahk

HaKayitz

HaKova Shelee Shalosh Pinot

Hashivenu

HaTikvah

HaTikvah ver.4

Hava Nagila

Hayoshevet B'Gahneem

Heenay Ma Tov

Het

Hevenu Shalom Aleichem

Im Zer Kotzim Koev

In the Window

Invei

Just One Shabbos

Klezmer tune

Kmo Az

Lagur Ethka

Lea - Dori Ben Zev

Shalom Aleyhkem

Shalom Hkaverim

Shimu Shimu

The High Windows

Yerida - Yehoram Gaon

Zum Gali Gali

Regards
John