Remap ctrl-j and ctrl-k in vim

Figure out exactly what escape sequence your terminal sends for Ctrl+arrow by typing Ctrl+V, Ctrl+arrow in insert mode: this will insert the leading ESC character (shown as ^[ in vim) literally, followed by the rest of the escape sequence. Then tell vim about these escape sequences with something like

map <ESC>[5D <C-Left>
map <ESC>[5C <C-Right>
map! <ESC>[5D <C-Left>
map! <ESC>[5C <C-Right>

I seem to recall that Putty has a default setting for Application Cursor Keys mode that's inconvenient (I forget why), you might want to toggle this setting first.

Note that although escape sequences vary between terminals, conflicts (i.e. an escape sequence that corresponds to different keys in different terminals) are rare, so there's no particular need to try to apply the mappings only on a particular terminal type.

You can use a special wildcard syntax with :set <Key> to let Vim automatically recognize xterm-style modified keys:

if &term =~ '^gnome'
execute "set <xUp>=\e[1;*A"
execute "set <xDown>=\e[1;*B"
execute "set <xRight>=\e[1;*C"
execute "set <xLeft>=\e[1;*D"
execute "set <xHome>=\e[1;*H"
execute "set <xEnd>=\e[1;*F"
execute "set <PageUp>=\e[5;*~"
execute "set <PageDown>=\e[6;*~"
execute "set <F1>=\eOP"
execute "set <F2>=\eOQ"
execute "set <F3>=\eOR"
execute "set <F4>=\eOS"
execute "set <xF1>=\eO1;*P"
execute "set <xF2>=\eO1;*Q"
execute "set <xF3>=\eO1;*R"
execute "set <xF4>=\eO1;*S"
execute "set <F5>=\e[15;*~"
execute "set <F6>=\e[17;*~"
execute "set <F7>=\e[18;*~"
execute "set <F8>=\e[19;*~"
execute "set <F9>=\e[20;*~"
execute "set <F10>=\e[21;*~"
execute "set <F11>=\e[23;*~"
execute "set <F12>=\e[24;*~"
endif

See :help xterm-function-keys and :help xterm-modifier-keys.