I normally just have each of my squads do one month of patrol/watch duty, than a month of training and then a month of offtime. I rarely have any full squads and prefer to keep them at 6-8 dwarves each. So far I have not once seen any dwarf complain about being on station for too long, then again, they had been training for quite some time before they ever saw patrol/watch duty assingments in Violentlash, because I just sealed off the fortress whenever a threat arrived in the first years.
By now I have 5 melee (2x5 and 3x8) and 3 archer squads (2x6 and 1x8). I have one room for melee watch duty, just in case I need a quick response team ready (though the room's access to the surface has become a bit long lately, I might want to give them a new exit, just in case some were-creature attacks or something), and 5 towers for marksdwarves to keep a look out for ambushes and such. The "defense room" is staffed by one squad each month, rotating through the squads, with the 5-dwarf squads taking 3 turns and the others 2. Before each "station" order they have one month of training and afterwards one or three months of free time (12/5 doesn't really work).
The marksdwarves on the other hand have split orders for the towers, as I only have 3 archer squads but 5 towers to man. As already mentioned before, it is safe to assume that only half of the dwarves ordered are at their post at all time. My orders for the marksdwarves look like this: "station-station-no order", with the first station being a split order for three towers, two dwarves per tower at least, and the second being a station order for the other two towers with 3 or 4 dwarves.
Overall that works quite nicely.
Anyway, I'm going away from the topic. The main point I figured out so far is that one needs to give the dwarves some time where they have no order. I had problems with my military getting stressed out, because they'd always see / get in fights in the caverns (before I closed them off) and their stress would never reduce because they'd always be stationed somewhere. Since I have quite a decently sized fortress, I just made a new squad and added offtime to the schedule that way.
From what I could see, this time away from duty is very important, both to not get bad thoughts for being on duty for too long as well as having some time away from fights and having some time to enjoy the good things of the fortress to reduce stress.
Dwarves will always be running to get food and water. Even if you forget to remove a station order given via the squad menu, they will run to get something to drink if they get too thirsty. I'd assume they also go sleep as well, never seen that though.