Vim has its own input method and keyboard layout.

Add this to your config:

set keymap=russian-jcukenwin
set iminsert=0 " English layout by default in input mode.
set imsearch=0 " English layout by default in search mode.

set langmap=ФИСВУАПРШОЛДЬТЩЗЙКЫЕГМЦЧНЯ;ABCDEFGHIJKLMNOPQRSTUVWXYZ,фисвуапршолдьтщзйкыегмцчня;abcdefghijklmnopqrstuvwxyz

Now you can toggle the layout with i_CTRL-^.

A handy trick: to type just one character available in the English layout without switching back and forth, press i_CTRL-V or i_CTRL-Q, type the character from the English layout, then continue typing in Russian.