Any ED that you are involved with as a Residency Program should not have a call room and if it does, you certainly should not be using it... if you are, then look elsewhere. The ED at any major house, at best, has a slight lull in the middle of the night... but that time is usually filled with chart catch up and maybe some email checks or catching up with each others lives. Remember that shifts are at most 12 hours... if you are working nights, then you should be sleeping during the day and should not even be tired in the middle of the night.
If you by chance moon light at a VERY small very rural ED, then you may in fact, catch much sleep at night. The Family Medicine residents where I came from would work at such places. They would usually work from 5pm friday to 5am on Monday morning. They would get TONS of sleep and see maybe 20 people over the entire weekend. Again, that was ultra rural/small town Texas. Any EM trainee should moonlight at places that are a tab busier than that as you can easily handle it.
As far as off service rotations (ortho, surgery, ICUs, ward services, etc) will be extremely variable on your particular house, particulay service, and the luck of the draw. You should, at most, be in house for 30 straight hours without sleep. And luckily, as EM residents, those days for our life can usually be counted on a few hands at most. I am in the MICU currently. I have had 5 calls so far (Q3). My worst thus far, I slept about 30 minutes, my best.. I watched two westerns in the evening, went to bed around 11pm after showering, and woke to my alarm at 6:30AM.
Just my .02...