Throw away all their toys! I'm serious - you need to put your foot down with drastic measures and show them whoes boss. Don't get soft when they cry. You are at war and you have to win. They sound spoiled.
hmmmm. "Siblings without Rivalry" would tell you to completely ignore their fighting, if the fighting is evenly matched and there are no real injuries.
And then, if you do have to separate them for fighting, give attention ONLY to the injured one, and not one iota of attention to the one who hurt the other. And even be sparing with the attention to the injured one - as in, "oh it looks like you have a scratch come here and I'll put some ice on it."
When you do send them to timout, make it short (30 seconds or so) but don't start the timer until they are still and silent. They can sit there for an hour and scream if they want, or they can be still and silent for 30 seconds. You need to have a clear visual, like a 30 second hour glass, and you don't turn it over until they are still.
I agree with Margy that they need daily outings with vigorous exercise.
what forms of discipline have you tried?
Seperate them up during the day if you can, do they go to any child programmes like My Gym and get some of their excess energy, walks to the parks, outside activities, they may be bored, also usually one twin is more active and very often starts the fighting if you can pinpoint this you can give her things to do away from the other one for part of the day, Get Dad involved with Games and outside stuff, lighter nights will be back soon and he can take them out and to the park for some fun and give you a break also at the weekend let him have them more so you have some time to yourself.