I feel your pain! Went through exactly the same thing with my three when they were younger, as what with breastfeeding, then teething, illness, nightmares, wetting beds and so on, I got to the point where I seriously wondered whether it was worth going to bed at all because I knew that I would be woken up so many times by one or all of them at some point in the night. ON top of that, we usually ended up with at least one of them joining us in our bed, so that didn't make for a good nights sleep either.
Used to obsessively count how long I had gone without a proper nights sleep and it mounted up to years.......... Was so tired I couldn't string a sentence together some days, because having been woken a couple of times, I couldn't get back to sleep and had massive sleep deprivation and no chance of a lie in to catch up. DH and I used to compete over who had had the least sleep! If he got up with one of them, he always seemed to have the knack of falling asleep again quickly, whereas I couldn't if I had got up because one of them was ill, because I would be worried they were ok.
BUT, it does eventually get better, just hang in there as best you can. It takes you some time to adjust to being able to sleep again, so be prepared for that, as I found that even when they eventually slept, I would still keep waking as it had become a habit.