Well, I would say that is is normal in the sense that many, many kids will have that impulse and give into it once or twice or for a period of time. Unfortunately, you have to deal with the additional complication of built in cheer squad and sidekick that is twinergy. (I am a sister twin mom--my boys are now 7, and their sister is only 17 months older, so when they were that age they ALL egged each other on).
First things first--safety. I am sure you have considered this, but just double checking--if they're using things in an unsafe manner then it's time for those things to go. Lamps are gone. (I assume you are not talking about an overhead light fixture) Any heavy or stick like toys--gone. Anything that would break your heart to have it destroyed--gone. Box those things up and put them away for when this phase is behind them.
Second--how much one on one time do they get with you, individually? I have found this to be THE BEST way to manage behavior problems in the long run, from two different angles--first for my own sanity, I get to spend time with each child and get to know them more deeply, in a context other than naughtiness. Yes, we all try to do that every day, blah blah blah, but when you are in the middle of a very horrible stage you are only human and that is damn near impossible. So, even if it's a "working date", you take one child on a errand (yes, even if the other screams the whole time with your partner/mom/dad/understanding friend). IME, the child and YOU will be all the better for it, and it's very good for them to see that it's okay for a parent to spend one on one time with the individuals rather than the unit.
Third--how are YOU recharging yourself? That too is extremely important, and in hindsight I wish I had cared better for myself in that regard when my kids were younger. Everything is made worse when you perceive that it is inescapable and when you are overy invested (because you have no other outet) in what your kids are doing. I am not a huge extrovert and hate going out, once I wised up I gave myself permission to waste 1 or 2 hours every night reading or playing on the computer instead of "catching up" on housework, reading parenting books that told me how crappy I was for not farting sparkles about my parental bliss, ect. Sometimes that meant staying away from internet stuff filled with Perfectly Perfect parents too. But for you, maybe it's going for a drive while your kids nap in the car and getting a drive thru coffee or whatever.
Hugs to you. Yes, you will get through this (don't punch me, I know how annoying it is when people say that, but you WILL.). Your boys are lovely, and they have a beautiful sweet mama. Maybe you just need to tweak your schedule a bit, and take a step back and make sure that everyone is getting their individual time and recharge time. Do you know if there is a twin group in your area? One of the best things for my boys at that age was to go on "twin trade" playdates--split them up and have them have a playdate with another set of twins--one of each pair at each house. :) It really broke up the dynamic, and I was glad that I made the effort to get to know other twin mamas.