I have no problem running E-sword through Wine.

1)Get the e-sword exe file from the e-Sword site and save it in your Home directory:

http://www.e-sword.net/downloads.html

2)(Assuming you have Wine already installed) get msls31.dll from here:

http://www.dlldump.com/download-dll-.../download.html

3) In terminal run winecfg
select windows xp
go to libraries, add, riched20.dll

4) copy msls31.dll to the system 32 directory under .wine

5) in terminal run "wine setup785.exe"

This will install e-Sword under wine.

An icon will appear in the desktop, but probably will not work. You'll have to direct it to e-sword.exe in the programs folder under .wine.