Guitar, you don't need the asterisk, since this is NOT used to mode a $3 but a $nick who initiates the command: !op me

To make $3 available, you need to enter: !op me NickHere as shown below:

on @*:text:!op me &:#:/mode $chan +o NickHere

You can also do it as:

on @*:text:!op me *:#: {

or

on @*:text:!op me*:#: {

<- but when you don't leave a space between the command and the asterisk, you need to make your $3 a double signs as $$3 so that mirc will ensure that $3 is specified before being triggered. Doing this will prevent an error.

P.S. You may need to make sure the $3 is on channel.