Basically, Nexus was never designed for easy wheel removal. It was originally designed for commuter bikes with full chain guards and wotnot -- the sort of bike people PAY other people to work on.
It was never aimed originally at the type of bikes it became popular on in Denmark - sporty, chain-guardless bikes - and which now seem to be catching on elsewhere. This led to endless problems with seals and water getting into the hubs - which all appear to be sorted now.
Anyway, back on track.
The easiest way to get your wheel off (and I can end up doing this several times a day) is to drop the shifter down to the lowest gear which will free up slack in the cable. You then tug on the cable outer so it hops out of its slot near the sprocket. Undo the wheel and drop it out of the frame and unhook the cable. DO NOT UNDO THE CABLE NUTS unless you can remember where to put it again - it is millimeter critical. Barrel adjuster is a red herring - it's easy enough to do without one. Thinking again was that it should be as sealed and low friction a system as possible.
Alternatively, take the wheel out, then undo the plastic lockring and pull the changer system (proper name is cassette joint) off. The yellow dots will show you how to assemble it again.
Compared to quick release and derailleur gears it's a fiddly system but compared with SRAM super 7 it's a dream to work with when you get the knack. I remember the original versions and they wer a nightmare and Shimano really have improved it a lot since then.