Why can host and nslookup resolve a name but dig cannot?

It’s the default behaviour of dig not to use the search-option.

From the manual page:

   +[no]search
       Use [do not use] the search list defined by the searchlist or
       domain directive in resolv.conf (if any). The search list is not
       used by default.

Edit: Just add +search to make it work, like dig +search myhost.