That won't have any effect on the problem (removing cookies). The problem is, in my opinion, most likely (like, 99% sure) linked with javascript. I had a firefox extension a while back that fucked me over with javascript, it would lag massively because it was trying to do some silly things and the forms here rely heavily on it.
Do you have any extensions installed on opera? Also have you tried over input forms? I found my problem was consistent across quite a few websites, including the input boxes here on newgrounds. How does the search bar for the forum and portal perform, do you get the same lag?
It could be an underlying problem with your install though, if neither of the above are applicable, have you tried a reinstall?