How do I map ctrl x ctrl o to ctrl space in terminal vim?

I've run into the same issue, the short answer is yes you can, and not only in the gui version. Adding this on you .vimrc is enough:

inoremap <C-Space> <C-x><C-o>
inoremap <C-@> <C-Space>

The problem seems to be that Terminal.app doesn't interpret <C-Space> correctly and Vim understands it as <C-@> which is a built-in mapping (:help CTRL-@).

Maybe you could go with something like the following in your .vimrc:

if !has("gui_running")
    inoremap <C-@> <C-x><C-o>
endif

which seems to work, here, but I don't like the idea of overriding built-ins like that.

Instead you should try with <Leader> (:help leader), it gives you huge possibilities for defining your own custom mappings and (depending on the mapleader you choose) won't interfere with OS/app specific shortcuts/limitations and hence be more portable.

With this in my .vimrc:

let mapleader=","
inoremap <leader>, <C-x><C-o>

I just hit ,, to complete method names.

The nitpicker broke pablox solution. The crux of the solution was just about remapping. So when you disable remapping, it cannot work.
If you really want to throw in a noremap, this is what it looks like:

inoremap <expr><C-space> neocomplete#start_manual_complete()
imap <C-@> <C-Space>

What will not work: inoremap <C-@> <C-Space> 'cause the <C-Space> part will not be remapped itself.

Add the following code to ~/.vimrc:

" Ctrl-Space for completions. Heck Yeah!
inoremap <expr> <C-Space> pumvisible() \|\| &omnifunc == '' ?
        \ "\<lt>C-n>" :
        \ "\<lt>C-x>\<lt>C-o><c-r>=pumvisible() ?" .
        \ "\"\\<lt>c-n>\\<lt>c-p>\\<lt>c-n>\" :" .
        \ "\" \\<lt>bs>\\<lt>C-n>\"\<CR>"
imap <C-@> <C-Space>

Source: https://coderwall.com/p/cl6cpq