I'll focus on Ctrl+Delete first.
The zsh command to delete a whole word forwards is called kill-word. By default it is bound to Alt+D.
How to make Ctrl+Delete do it too depends on which terminal emulator you are using.
On my system, this works in xterm and Gnome Terminal:
bindkey -M emacs '^[[3;5~' kill-word
and for urxvt, you should do:
bindkey -M emacs '^[[3^' kill-word
If that doesn't work, try typing Ctrl+V Ctrl+Delete to see what the value is on your system.
You could even add both of those together to your .zshrc, or use the output of tput kDC5 instead of hard-coding the sequence.
Ctrl+Backspace seems harder.
On my system, pressing that is the same as pressing just Backspace.
If yours is the same, I think your best option is to use Alt+Backspace or Ctrl+W instead.
Ctrl+W is the standard "kill word" (aka werase).
Ctrl+U kills the whole line (kill).
You can change them with stty.
-bash-4.2$ stty -a
speed 38400 baud; 24 rows; 80 columns;
lflags: icanon isig iexten echo echoe -echok echoke -echonl echoctl
-echoprt -altwerase -noflsh -tostop -flusho pendin -nokerninfo
-extproc -xcase
iflags: -istrip icrnl -inlcr -igncr -iuclc ixon -ixoff ixany imaxbel
-ignbrk brkint -inpck -ignpar -parmrk
oflags: opost onlcr -ocrnl -onocr -onlret -olcuc oxtabs -onoeot
cflags: cread cs8 -parenb -parodd hupcl -clocal -cstopb -crtscts -mdmbuf
cchars: discard = ^O; dsusp = ^Y; eof = ^D; eol = <undef>;
eol2 = <undef>; erase = ^?; intr = ^C; kill = ^U; lnext = ^V;
min = 1; quit = ^\; reprint = ^R; start = ^Q; status = <undef>;
stop = ^S; susp = ^Z; time = 0; werase = ^W;
-bash-4.2$ stty werase ^p
-bash-4.2$ stty kill ^a
-bash-4.2$
Note that one does not have to put the actual control character on the line, stty understands putting ^ and then the character you would hit with control.
After doing this, if I hit Ctrl+P it will erase a word from the line. And if I hit Ctrl+A, it will erase the whole line.
Best Answer
Here's a snippet from .zshrc i've been using:
I recall this was the original source: http://www.zsh.org/mla/users/2001/msg00870.html