It is a socket not a nut. You use the socket to remove the nut. There is a key lock holding the nut in place. You can either remove the key, use a razor blade and a magnet, or just break the nut. I do not recomment breaking the nut because you will have to replace it ($30) and you could damage the spindle, plus the key is easy to get out.
The vehicle does not have to be in park or neutral to engage the 4x4. Some people believe this because they may hear a loud "clunk" when the system engages. This is normal and accounted for in the design. You can engage your 4x4 at any speed, but it is not designed to run faster than 55mph. to avoid the "Clunk" take your foot off the gas then press the 4x4 button.
Before you start taking anything apart make sure you need to. First of all make sure that the system is not engaging and it is not the light. If it is not engaging have the vehicle off, but the key in the run position. Push the 4x4 button and you should be able to hear the t-case try and engage. (remember the system engages at 2 point the T-case and the hubs) If you do not hear a sound check you switch. If you do then it is probably your hubs. Depending on many factors you really shouldn't have to clean out the hubs. so first check for anything broken.
If you do decide to clean everything do it all the way. Take off your bearings and re-pack those. I have done two levels of cleaning, a simple wipe off and and a heavy degreaser. Either method works it just depends on how much time you want to spend. When taking everything apart make sure you place it so that you can assemble it again correctly, get a hanes manual. Check to make sure nothing is broken, use clean grease but don't shovel it in. Too much grease can actually cause the hubs to not engage and cause damage. most importantly put the hub back on correctly. With auto hubs they will only set in flush in one position. the hug should be flush with the rotor, in the wrogn position you can push them flush, but this is wrong and will cause them to break.
good luck
