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Looks like I'll have to do the rear sway bar links on my wife's 2003 Honda CRV.
My CR-V is a 1999 and I replaced both front and rear sway bar links a couple of years ago, making them older than the ones you are taking off. Could be because I Krown my car, but I remember those nuts being dry.
I had no problems taking mine off. You do have quality box-end wrenches? Don't use an open-end wrench. Also, the joint has a hex to use a wrench on to keep it from turning. Make sure the hex key is fully inserted; that means, pick the dirt and rust out of it.