How to rebind keys to key combinations?

I really would like to switch to Linux, but there is still this one last thing I just can't get working. On Windows I'm using autohotkey to rebind some keys to key combinations, and I'm just too used to it to use the system without it.

I'm using the following bindings:

LAlt + j = LeftArrow
LAlt + k = Enter
LAlt + l = RightArrow
LAlt + i = UpArrow
LAlt + , = DownArrow
LAlt + Shift + j = Ctrl + LeftArrow
LAlt + Shift + k = Shift + Enter
LAlt + Shift + l = Ctrl + RightArrow
LAlt + p = Backspace
LAlt + [ = Delete
LAlt + Shift + p = Ctrl + Backspace
LAlt + Shift + [ = Ctrl + Delete
LAlt + c = copy
LAlt + x = cut
LAlt + v = paste

I have tried using the Linux equivalent of autohotkey - Autokey, but it's too high level to be usable, even in Firefox up and down arrows won't work like they should.

I have also tried xmodmap, but it seems to be impossible to achieve my bindings with it.

Any suggestions?

Know someone who can answer? Share a link to this question via email, Twitter, or Facebook.