From a working EFI boot of Linux (even from an emergency disc), you can use the "efibootmgr" utility to add whatever NVRAM entries you had to launch each distribution's boot loader back to the NVRAM. Alternatively, if you've got one distribution's boot loader working, you may be able to get it to either chainload the others or to load your other distributions' kernels directly.
Check the man page for efibootmgr or this page
for information on that utility. You can check other sub-pages from that one for information on various specific Linux EFI boot loaders and boot managers.