I haven't read all of the replys yet, but what I did when I was desperate for sleep with my kids was to put a matteress on the floor against a wall in their room and go to sleep in there, but put them in their cot first and tried to go to bed early-ish (about 9 or 9.30), so if they had a good night and slept til midnight or whatever, then I would get a fairly good uninterrupted bit of sleep before having to worry about them getting up. And then I would put them ont he mattress with me between me and the wall.
Good luck. Sleep deprivation is seriously torturous. I feel for you.