Yes you need to loosen first then remove nut when car is up off the ground. can't remove strut without doing so.
Also much easier to remove strut if you take the cowling and everything out of the car from under the hood. the top plastic and metal bottom right below the window. it's easy and only a few bolts.
also get and use.
Black & Decker Ready Wrench Model MSW100
http://www.walmart.com/ip/Black-Deck...SW100/12520389
You can get it at walmart for like $25 and it works perfect. and much better than a box end wrench and allen wrench.
You still need the allen wrench but if you put this tool on the right socket size and put it on the nut, then you can fit the allen wrench straight through the socket into the allen key hole on the strut. This tool will sit full over the nut like a socket and not at a weird angle half on teh nut like a box end wrench.
Hope the explanation is good. I can't find a better picture but basically the tool is like 8 sockets in wrench form.