For a solid-body electric guitar, or other guitars where the strap connects to the body, hanging it from the strap should be absolutely fine. The body is relatively rigid, and as long as you don't bash the neck around it should suffer no damage.
Where the strap connects to the end of the neck I would be more worried of long term stress on the neck.
I hang most of mine from wall mounts, acoustic guitars facing the wall (as they have thick bodies) and electrics facing away. There is little stress on them in this position, however you may end up with marks on the headstock from the rubber mounts.
Best all round, if you have the room, appears to be a guitar stand, however my worry with these is that you may trip over them or the strap - which always seems to end up in a foot sized loop.
If you have no stand at all, my core focus would be that it can't fall, so propping the guitar in a corner would be recommended, and if you can't do this, place it string side to a rough object to get some friction.