Can a person whose driving was evoked at IL because of DUI get driving license at Canada?

Yes, if you're a citizen

If you move up there to live, then you can apply Now of course normally they will not issue you one, until the other license has been cleared.

No.

First of all here is the definition of evoked:

e·voke (-vk)
Tr.v. e·voked, e·vok·ing, e·vokes
1. To summon or call forth: actions that evoked our mistrust.
2. To call to mind by naming, citing, or suggesting: songs that evoke old memories.
3. To create anew, especially by means of the imagination

You mean revoked. And, as a Canadian citizen and former automobile insurance underwriter, I truly hope that you can't come here and get a license if yours was revoked due to a DUI. My personal feeling is that once you are charged with a DUI you should never be allowed to risk other peoples lives again, not giving you a drivers license would accomplish that.