Do you use the latest graphic drivers?
Did you try to unistall, reinstall and update EF?
are you using a pirate/cracked version of COH?
[......]Dude... did you installed EF in the correct path?because the last warnings.log you uploaded says otherwise:WORKING-DIR E:\Steam\steamapps\common\company of heroes beta
[CoH:EF-Dev]Walki: BULLSHIT[CoH:EF-Dev]Walki: I'll eat a tree if this won't work now[CoH:EF-Dev]Rizz: ok[CoH:EF-Dev]Rizz: I'll hold you to it<10 minutes later>[CoH:EF-Dev]Walki: I think I really gotta eat a tree...[CoH:EF-Dev]Walki: got a decent one?
Ah! You installed it to CoH Beta (retail beta) which isn't supported yet. We need to make one change to support it, but it will stop supporting current version. Please use 2.601 and not 2.700 Beta when playing EF.