Unfortunately, it is often that way with newborns, and it's double the load with twins. My first few months with my twins was a terrible fog of sleep deprivation and crying and endless diapers. I remember being convinced that it was never going to end, and convinced that I was going to drop dead, but it does and you won't. It passes before you know it. In the meantime, you gotta find ways to cope as best as you can. Are you nursing them lying down? If you can get one twin to sleep, you can lie down and latch the other one on and sleep through most of the nursing. I used to put one on each side of me and roll back and forth during the night to respond to whatever twin was stirring.
Have you introduced a pacifier? The usual advice is to wait until 6 weeks or longer, but if they're latching well and have regained their birthweight, you might consider doing it now if you're truly going nuts. The paci really helped my DD2 get some sleep, which left me free to attend to her brother. He never would take a paci, but at least one of them would and that helped a lot.
I didn't notice if you had any older kids. Can you get some sleep during the day while they're dozing? Also, getting DH or your partner or someone else to take one for a short time, in a sling or carrier, can give you time to regroup. A nice brisk walk outside in a carrier will often soothe a fussy baby, and it's good for them to learn to take comfort from the other parent.
You can try helping them to straighten out night and day by keeping the house dark once the sun goes down-- just a few dim lights. And in the morning, make sure and get them outside, even just for a short time, to expose them to bright daylight. That helps set their internal clocks. It takes some time though for newborns to get day and night sorted out, and it'll be three or four months before their sleep starts getting consolidated and they start sleeping regular hours.
And seriously, a mama of newborn twins should be doing nothing but caring for herself and the babies. Do you have someone-- your partner, a family member or friend or neighbor-- helping you with housework and feeding you and your family and stuff like that? In the early months, you have nothing left for doing stuff like that. You have to spend every spare minute you can sleeping and taking care of yourself, so that you can be there for the babies.
good luck. I have nothing but the greatest sympathy for you. I still have such clear memories of how difficult it was in the early months, and I wish there was more I could do to help.