How can I repair EFI? The computer is a MacBook Air. I have OSX Yosemite and Linux Ubuntu 14.04 dual boot. I messed up and damaged my Mac EFI and hence OSX ceased to work. Recovery disk was destoyed too. FileVault is on and I just changed my login password (which I remember but can not use) before the problems appear.

Please help..
If you have access to another mac, you can make a yosemite bootable install usb. http://liondiskmaker.com/ has a applescript program that will creae one, you just need a usb stick with 8gb and the installer downloaded. 
Boot the messed up computer from the USB stick by holding shift during the boot sequence and selecting the USB stick. 

There you can restore from time machine if your time machine works. Otherwise just reinstall over your old install. It shouldn't delete data but messing with the EFI is always dangerous and might need to be repartioned. 

If that is the case you could try booting from an external mac, either with a harddrive that has mac, or time machine etc, and with that you should hopefully be able to mount the messed up disk partition that has the data and get your data off it.