Light will no doubt tell you to keep them in their cases, with a humidifier. Good advise, for sure, but my personal opinion is that is not really necessary for solid-body electrics. (Just for grins, and to check my hypothesis, I checked the fret ends on all my guitars- only one that was less than smooth as a baby's butt was a cheapie.) I am 100% behind keeping one's acoustic and hollow-body guitars properly hydrated, and have been casing my acoustics- simply because it is easier to do than hydrating the whole room- I've tried both, to good effect all around. (As it happens, my music room has been at about 35-40% relative humidity, without any artificial efforts on my part, for the last few weeks, so I figure I am golden for now.)
I keep all my electrics on wall hooks- been doing so for over a year, and have not experienced ANY ill effects. Most shops keep ALL their guitars on wall hooks, solid and hollow bodies, electric and acoustic, archtop and flats, etc. until they sell. BTW, one of my guitars is an... Epi Les Paul. Also have a Westone Thunder and I had a Westbury Standard (very LP-like weight, both). I also am cheap, so I use hardware-store u-hooks. They don't stand off from the wall as far as expensive guitar-store u-hooks, and the hardware-store hooks look more utilitarian, but the only drawback is they put the headstock up against the wall, so one or two tuners might get turned a quarter turn when I put the guitar there, and it leaves a smudge against the wall (which is not seen when the guitar is there, anyway.)
As to detuning, I am of the opinion that even 4 weeks is not long enough to get any longivity benefit from detuning, and that the time spent detuning and extra time spent re-tuning is not worth what benefit detuning might bring. Detuning that often may be a disadvantage- you prevent the guitar from getting accoustom to a particular tuning tension, thus it is always in transition. You would also have to re-stretch your strings every 4 weeks, which will cost you MORE time retuning, and probably shorten their life, too.
Concusions:
1. For your use habits, don't detune;
2. Nothing at all wrong with wall hangers.